Frankly I'm not too sure about analysis, etc.
For starters it all boils down to what you personally know. If you know harmony you could analyse some Chopin, some Beethoven, both harmonically and melodically and form wise. We keep talking about the sonata form, but what is it? Check wiki (not an academic tool really, but excellent for what it is), and try to see what is going on in Mozart or Beethoven or Haydn sonatas. Where's the first theme, where the second, etc...
In all, when you end up, after an excersize in a result (output), a score, a text, a midi file, whatever, you usually need someone to check if you're right or wrong (in the case of analysis and strict rules, cause in composition there is no 'right' or 'wrong'). It's one thing to learn music theory (the basics) from the Internet and books and a little orchestration, but unless you have someone with experience by your side, things are going to get more difficult as you move further into the depths of musical knowledge.
So start ahead (if I'm assuming correctly your level of understanding music (since you mentioned Piston and Knud). Grab an early Beethoven Sonata or a Mozart/Haydn one and try to see what tonality it's in. Then move to see what is the main theme, if there is (there is...) a second theme, where does it enter. Is it in the same tonality? Then try to understand the underlying harmonic progression. For example the 6th Beethoven Sonata starts with some chords in both hands. Goes from F to C7 (so from I to V, because we are in F major tonality), then puts a little F7 (with Eb) and goes even further into the Bb (IV) and so on...
If you find the above too hard go fruther back into smaller works, and earlier times (still classic period though). If you find them too easy move ahead in time and see what you can do with Chopin and his expanded harmonic vocabulary. And then try Debussy if this is too easy as well.
The above are some ideas, based on pure assumption on someone I don't know, so take them with more than a pinch of salt. I could be dead wrong to assume what you know or don't know.
The other idea would be to list what you do know and don't know (think you don't know anyhow), the books you HAVE read, and the works you HAVE written. This would give me and the others a very definite idea on where you could move next to.
Just in case you don't know it: www.imslp.org
. The definite collection of FREE (legally free) scores. In PDF format and there's also a printing facility there I think.