hey rider!
if you want some real help with this, why not we do together an analysis? choose a sonata you like, and let's do it online.
i'm not a scholar but i have several years (and several sonatas) of experience, and if i can help you in anyway, it would be a pleasure.
there are a basic misconcept that maybe is bothering you. some textbooks talk about "theme" but this is a very narrowed view of the sonata. you must think about regions, because a sonata is much more a debate of tonalities than melodic material. of course this have its impact, but it's not the fundamental one.
so, you normally have something like this:
- thematic region 1: in the tonic (one, two or several themes). it ends when a major unstable part begins;
- transition (or bridge): the name of that part, where a modulation takes over.
- thematic region 2: contrasting key (dominant, relative). again, you may have one to several themes (sometimes it is only the thematic region 1 transposed);
- closing theme and coda: although not always present, it is very likely to find a very contrasting mood into TR2. that is called closing theme. also it's very common a coda to bring the whole exposition to a close.
- development: here the composer contrast the ideas, in a (very) chromatic and modulatory section. notice that some composers use material from each or any part of the exposition and sometimes even includes new material.
- recapitulation ("reexposition"): given two contrasting ideas and the field to develop their contrasts, rhetoric principles say you must bring this to a close. that's the function of the recapitulation. pay much attention because there are no rules here but end in the tonic (the fundamental contrast since 99% of the sonatas' expositions ends off tonic).
it is normal to find a new development, reordering, even new material: it's all up to the composer's imagination.
and about formulae...dude, this doesn't exist. write down the structure of a sonata and analyse the next one...and the next one...for sure you will find similarities but there is no two sonatas exactly alike, especially due to the fact that sonata is not a form but a composition technique (the best parallel is the fugue, and is no coincidence that this kind of composition ruled during the late polyphonic era, and the sonata "replaced" it from the classical period).
well, it's up to you now!