Sand with 80 grit
Sand with 120 grit
150
180
220
280
320
buff with tripoli compound
buff with white rouge compound
If you aren't patient, don't bother It's a pain in the ass when you're just learning, and sometimes even when you know what you're doing.
For polishing, I use a drill with a buffing wheel attached (3/8" arbor on it). Use one for each compound, too. The key is sanding to get it smooth, otherwise it won't be mirror-reflective. It'll shine but not be smooth and mirror like.
Prepare to spend lots of hours on that, especially for your first time doing it. Once that's done, break out the drill and get to work. If you smudge compound on the piece, you're using too much. Just work it into the piece and remember how much NOT to use next time.
Once you get through with the tripoli, it will shine and but smoother than you left it from sanding. That's its job. The white rouge is used to bring it to a mirror shine.
If you do a search on "polishing", you can find more tips too. This stuff comes up all the time.