I assume we're not talking about classical, based on the context clues in your post? It might alter the way I approach the answer.. we talking blues/jazz lead sheets? Printed ragtime? Improvisational stuff?
Printed ragtime. But realize, like Baroque music, it has an improvisational tradition as well.
No worries, ragtime is one of my favorite genres. Were you part of the "ragtime" vs "stride" thread a while back?
This is easiest to show if we were able to sit down at a piano and look at a piece. Let's take Scott Joplin's Maple Leaf, since it's a standard and I'm hoping you're at least familiar with it, even if you don't play it.
If I'm looking to sight-read this score, I'm going to do the following:
1. It's in Ab, except for one section in Db
2. The opening theme repeats 3 times, so I'm paying especially close attention to it
3. The opening is Ab, Eb7, repeat, Fdim, repeat, Abm, repeat, [Bm7, Ab, Fb maj (Emaj), Ab, Eb7, Ab], repeat bracket
3a. I can already see that I'm going to keep my index finger on the Ab in the bracket section, so the Bm7 to Ab change is very very small (half steps on thumb and pinky). Same thing for Fmb/Emaj and Eb7. All very small movements.
4. Look at the left hand beat.. octave, octave, chord, chord, repeat.. pretty standard stuff there
5. Now, I look at the right hand. Doesn't really change from notes actually in the chords represented. So, I look at what position. Ab is 2nd inversion, Eb7 is root. Fmb/Emaj is root, Abm is root. Bm7 is 1st inversion.
So, there really is nothing getting "throw at you" in the opening theme.
Looking at the 2nd theme, we've got some chromatic octaves and some arpeggiated stuff. But all standard, and nothing out of the ordinary.
Then, we repeat the main theme.
Then we get to Db. Not much different than Ab. In fact, the section starts in Ab7. So we're still dealing with I-V7, or in this case, V7-I. (Notice, I'm not getting overly complicated in chord names, naming every single change, etc.)
In the first 2 bars, the thumb changes position. In the next 2 bars, the 2nd finger goes up to a Db, and the thumb continues the change from the first two bars.
This whole thing repeats, then it modulates to Bb and follows the same pattern. Then, it does the same pattern in octave form (root-2nd-root that the thumb did before)
There's really only one odd measure out, with the syncopation in the LH. So, I look at that specifically and notice it's a Gdim6.
Last section goes back to Ab, but notice it starts in Db. In this section, you've got Db, Ab, Eb7. Notice it's all 1-4-5.
So, that very basic, 2 minute overview of the piece tells me what chords, and what progressions, Joplin uses in the rag.
Knowing ragtime like I do, I know that you're typically going to play a LH stride using either 1-3-5 octave, and then either root, 1st, or 2nd inversion of the chord. Typically, when you play the root octave, you won't play the root chord. The most common is root/5 with a 2nd inversion, and then probably 5/root with a root7.. so root-2nd-5-2nd.. or in a V chord, 5-root7-root7-root (octave lower). The reason for this is the octave there sets up the root of the I chord. (Look at 2nd measure of Maple Leaf for an example of this.)
Now, I'll touch on improvisation..
I actually believe the best way to learn to read ragtime is to improvise ragtime. (This probably goes for all music, but I have a real tough time improvising classical.)
You will get very comfortable with chord changes, little half-step raises and drops to get to the next chord in the progression, little ornaments that help make those changes, modulations of chords, etc.
Best part: if you don't have an ear, you can do it almost entirely academically. (Obviously I recommend some ear training, but if you just can't get the ear in line, it's not the end of the genre. It's highly academic at its root.)
To take the improv back to the music.. when I look at the rag, I see the following technical difficulties:
1. Stride bass
3. octave work
4. repeated chords
5. alternating octaves with notes/couples
That's about it. So, if you have a technical difficulty, look at which one, and then take it over to the improv side. Don't try to solve it in the piece itself.. you'll screw yourself up. (You tense up when you have to hit a "specific" note. When you improv, mentally, you accept mistakes and tend to correct them more fluidly. Then, when you go back to the piece, you weren't learning the technique while practicing the specific notes in the piece incorrectly.)
I hope this was a little helpful. Like I said, I wish we could just sit down and talk about it, but I tried to be thorough (without being long-winded) and give some examples that might help. Steer me from here.. what made sense? What didn't? More examples? Etc.