Traditional approachs to form typically introduce the practice of formal analysis through a series of specific forms and explore form through the lens of that form. While this approach can be highly functional within the specific forms introduced, it limits the imagination by starting with specific forms, instead of starting with the concept of musical form in general. Starting with specific forms, implies that all pieces have existing names and that it should be possible to find the name if you look, and if you don't find it, you probably just missed it. However, plenty of pieces don't fit into one of the existing categories, and more importantly, pursuing form through specific form names is style and genre specific, meaning that most approaches to form stay within the bounds of a particular style. Because most musicians are interested in a multitude of styles, a style-specific approach prevents them from enjoying formal analysis in styles they haven't studied in particular and I believe that to be a mistep worth correcting.
The approach I've outlined below focuses instead on the process of formal analysis in general and is inspired in part by Brent Yorgason's wonderful software Audio Timeliner. As Brent argues and demonstrates with his software, musical form can be explored in a multitude of styles through the same basic approach. His software led me to the question, "if form in classical music is so different from popular music, then why does using Audio Timeliner feel so natural in either style? Doesn't that mean that there's a great overlap between musical form in general?" My approach embraces this similarity and formalizes an approach to form that focuses on function before directly engaging with form-specific terminology.
This approach is also particularly inspired by Jay Summach's dissertation "Form in Top 20 Rock Music, 1955-89" (Yale University) which envisions form in a hierarchical and functional manner, and introduces the concept of "Core" and "Auxiliary" modules which he categorizes all other formal "modules." My approach expands his core and auxiliary approach to form into classical music and combines their similar aspects.
Disclaimer: The steps below are a logical and recommended way to proceed with a formal analysis regardless of the style. However, you may find it more natural to do things in a different order depending on the circumstances. For example, it's incredibly common for popular songs to start with some form of prefix ("intro") so labeling it as such before you've made other larger decisions might just seem natural. Similarly, the first movement of most late-18th century, Classical instrumental works are in sonata form so you might prefer to start by labeling the first section as the Primary Theme or Exposition (assuming it doesn't sound like an introduction). You'll find that knowledge of a style is something you always bring to the table, so it's fine to use that to your advantage, just be aware that such pre-conceived assumptions can blind you to the actual form because you've become too detailed before it was appropriate. For example, though the great majority of Mozart's multimovement, instrumental works start with a sonata form, K. 331 doesn't.
In general, allow your formal analysis to come together by thinking in less specific terms first and then slowly moving toward a more specific analysis. This will fend off the possibility of a specific formal label limiting the scope of your imagination as you work. For example, if a composer writes "Rondo" at the top of the piece don't start your analysis by hunting for an ABACA form. In 18th and 19th century Classical European music, composers used the term Rondo to mean that a main theme or refrain will recur throughout the work, separated by music that is not that theme. This results in a wider variety of formal possibilities than just ABACA and, importantly, it includes the often used "Sonata Rondo." There's nothing wrong with keeping these formal arrangements in mind, but you want to avoid having a specific label too early in the process. A similar issue can crop up in Verse/Chorus form and Sonata form. In Verse/Chorus form, the first section might be the chorus or postchorus but if you start out by deciding the verse is the first section (which is usually the case) you'll have to back-track. With Sonata form, you don't want to decide right away that the first section is the primary theme, because in many cases sonatas have slow introductions before the primary theme begins.
Though, it seems natural to start by applying letters starting with A, a better practice is to start with the more general approach of showing relationships with color or texture first. If the first section is repeated at some point, use the same color for those sections, instead of labeling with A and A. This helps to avoid having to backtrack because a specific label was used before that level of specificity was appropriate. For example, if the form has an introduction, the practice of labeling the first section as A would lead to all subsequent sections being labeled incorrectly because of this one false step. Instead move from general to specific by starting with colors or textures. If you color the first section blue, that won't need to change when you've discovered that it functions as an introduction.
Once you've segmented the piece and decided upon relationships with color or texture, then really think about the function of each large section you've identified. It should be pretty easy to decide if a section is a core section (main or contrasting) or an auxiliary section (connective or external), though there are two important things to keep in mind at this stage: (1) your familiarity with a given style will start to play a bigger role now, and (2) each piece also has an internal, relative set of relationships. For example, while the B section of a rounded binary form is associated with instability, stability can be measured in terms of a continuum of all stable and unstable music that you've heard in your life and the relative level of instability of this section when compared with how the piece in question begins. Even just starting on the dominant when the A section started on tonic would usually qualify as relatively more unstable. So, make sure to be aware of which scope your focusing on, the scope of your entire life or the scope of an individual piece. During this stage, you're likely to start considering some named forms and their associated formal layouts. Again, I would caution you to avoid getting too specific too soon. Instead, try to make decisions about function for the majority of the piece before slapping on an over-arching formal label because doing so too early can blind you from the reality of the piece.
Before turning to the specific labels associated with a style or form, I wanted to say something about formal labeling in general. Because in most situations you're going to be able to say that a section is accurately represented by a label, it's easy and natural to assume that every section should have one and only one label. However, in many cases, music is actually more flexible than that. A section can actually start one way and clearly suggest a particular label and then end in a way that conflicts with label of the first part. Janet Schmalfeldt's work on the "process of becoming" has been instrumental in promoting this perspective (note that this symbol ⇒ is used to denote becoming). So, instead it's best to think of the formal labels as adjectives describing some group, allowing for multiple adjectives to apply. Again, the great majority of musical sections you'll encounter can accurately be described by a single section label, but embracing the perspective that a section can be described with multiple—most often consecutive—formal adjectives is a powerfully tool that opens an analysis to embracing the nuance of the work at hand, instead of reducing its more unique shape into a single, unsatisfactory container. This can happen in a Classical sonata form, for example, when there seems to be no clear division between the primary theme and the transition (a boundary typically marked with a clear cadence). The first movement of Mozart's K. 545 is a good example (P ⇒ Tr). Also in Classical sonata form, the secondary theme and closing sections are typically divided by a clear PAC but sometimes no clear division exists and instead clear rhetoric associated with closing sections ensues, suggesting that an accurate reading would be a single formal section that starts as secondary theme and ends as a closing section (S ⇒ C). This adjective perspective can also be used less formally, to see that you believe a section is mostly behaving like a typical section but that it contains the rhetoric of another section. For example, "the secondary theme was notably calm because it began with elements of a suffix including a tonic pedal." (see the secondary theme of the first movement of Mendelssohn's violin concerto as an example)
Now that the piece has been segmented into large sections, the thematic relationship between those sections has been decided upon with color or textures, and the function (or less commonly, functions) of those sections has been determined, it's time assign letters (A,B,C, etc.) or generic labels (prefix, suffix, transition, retransition). At this stage, you may start to have clear evidence for a particular form and may elect to use the specific terminology associated with that form instead of writing down something that you know you'll just be changing later. However, the form of a piece doesn't necessarily have a specific name like rounded binary, 32-bar song form, or theme and variation. In those cases, the "name" of the form is really just the layout of the capital letters you've decided upon. It's common practice to leave Auxiliary sections out of the name when doing this. So, an A B C A form with a retransition between C and A would just be referred to as "ABCA" form. A lot of people are uneasy to walk away from a formal analysis without producing a specific name because they feel they might just be missing something, however both situations are possible: you might have missed nothing, or you might have missed something.
Determining the relationship between sections is often a simple same-different task. If the section is the same music as another section, then they should share the same letter, if it has different music then it should get a different letter (typically, the next letter in the alphabet that hasn't been used yet). In practice, the difficulty of this process is on a continuum of clarity from obvious to ambiguous. It is common to use apostrophes (A', A'', A''', etc.) and super-scripted Arabic numerals (A2, A3, A4, etc.) to express difference. Admittedly these are blunt tools, but the apostrophe typically means the sections have differences in melodic embellishments, octave, instrumentation, and/or texture but usually have the same melody, harmonic structure, and phrase structure, though it may have short expansions but they generally shouldn't cause you to forget which section you were in. The super-scripted Arabic numeral is used for more substantial changes in melody, harmony, and/or phrase structure. If the first A section, for example, has two phrases (a b) but the second A section has a completely different second phrase (a c) or even new phrases (a b c d ), then the second section would be designated as A2. This level of change could also include a new modulation or more substantial expansions. If a section seems to be the combination of two other sections (it's rare) an ampersand ("and" sign) can be used to demonstrate the duality (A&B)
Another set of symbols that is historically used with variation form are Roman numerals, which designate each variation. Typically, the theme is called "theme" and each variation gets its own Roman numeral (Variation I, Variation II, or Var. I, Var. II). In more conservative sets of variations, the Roman numerals are basically equivalent to the apostrophe symbol concerning the types of changes, but variations may also involve more substantial changes, but the notation is the same. So, each Roman numeral only capture the fact that it is a unique version of the theme, but doesn't capture the type of change.
If you recognize that the formal arrangement you developed is related to a form with a name, then it's time to convert the generic labels into form-specific and/or style-specific terms. Just to reiterate an important point, if you've made it this far, you already know the form of the work because a work can have a form even though that form doesn't have a name. The advantage of engaging with the form-specific terminology, is that it deepens the connection between your understanding of the current piece and how it compares with other works that are also in that form. Even just for simple comparisons it can be a very powerful tool. For example, the expression, "I've never seen a sonata with a transition this long!" contains a lot of information about your understanding of a style and how your piece compares to that model. For comparison, a more abstract statement like "this transition is 15 seconds long!" doesn't carry much significance because we don't have context to compare that amount of time. Is 15 seconds long or short? When combined with a particular form, however, it takes on meaning relating to expectations for that form. A 15-second transition in a sonata is compartively short, but a 15-second transition between a minuet and trio would be very surprising because it's not even part of the style for them to have a transition at all.
You can convert the generic labels to form-specific ones either through your knowledge of the form, or by selecting the appropriate terminology by comparing the abstract model of the form to the hierarchical diagram of formal sections. For example, if you've decided you're looking at a sonata form, then you'd convert the stable contrasting section into the "Secondary Theme," or if the work started with a prefix before the its A section started, then it would be converted into an "Introduction" and A would become "Primary Theme."