Sounds to me like you just need to write, edit, and read more.The best I can prescribe is to read Stunk and White's Elements of Style, then go through your work line by line and try to implement their guidelines.
Renni Browne and Dave King's Self-Editing for Fiction Writers is also chock full of editing exercises. You might want to check that out. They have editing exercises, with suggested answers, so you can compare your choices to theirs. They cover "show and tell"; "characterization and exposition"; "point of view"; "proportion"; "dialogue mechanics"; "see how it sounds"; "interior monologue"; "easy beats"; "breaking up is easy to do"; "once is usually enough"; "sophistication"; "voice". I highly recommend their book as a tool to gain insight on your writing.
As for plots and deciding what's necessary--one exercise I read about (can't remember where) is the following:
Summarize your story in one sentence.
Make a list of scenes in your story with a one-sentence synopsis of what happens in the scene.
Next to each scene write what that scene does in relation to your story summary--establishes character, sets up plot, etc etc.
Delete any scenes that don't do anything to further your story summary.
Consider deleting scenes that only accomplish one or two things and reworking those objectives into other scenes.
As for excessive prose... Strunk and White will take care of that. The only remedy is to go through your piece line by line and try to figure out what you can cut, how you can reword for fewer lines. Attacking adverbs and adjectives is a good start.
In journalism school we did one exercise where we wrote a 1000-word story. Then we cut 500 words. Then we cut 300 to end up with a 200-word story. Obviously, you have to rewrite stuff, you can't just cut. I think this exercise could be done in fiction, though maybe to not such an extreme. It really forces you to really focus on the story.
[This message has been edited by annepin (edited February 06, 2008).]
[This message has been edited by annepin (edited February 06, 2008).]