I've never taken the SAT, but I did take the GMAT. IIRC I used books by Kaplan and The Princeton Review.
Preparation absolutely did help. I didn't develop any new generally-applicable skills, but I did:
1. Practice the style of essays these tests require.
2. Improve my speed at spotting specific types of incorrect answers.
3. Learn a few grammatical rules that were different from the way I learned English growing up. (It was a long time ago, and sadly I don't remember the specifics.)
Preparation absolutely did help. I didn't develop any new generally-applicable skills, but I did:
1. Practice the style of essays these tests require.
2. Improve my speed at spotting specific types of incorrect answers.
3. Learn a few grammatical rules that were different from the way I learned English growing up. (It was a long time ago, and sadly I don't remember the specifics.)