Nick, I'd hardly call myself an expert given the talent on this forum, but I've had pretty decent success polishing my models. Make sure you've laid down a few good coats of colour to help prevent burning through to the primer.
I start with a 4000 grit polishing cloth, and move through 6000 and 8000. Make sure the cloth/paper is well soaked in warm water with miild detergent and gently sand. Once done, rinse it and let it air dry.
I then use Tamiya polishing compound, but you can use any automotive polish but not a "cut and polish" since I find it too abrasive. Apply a small amount to the model, then use a clean, soft cloth to gently polish in small circles, being careful of raised edges. Don't rub all of the polish into the model though. You need to let it "haze dry". So gently rub it in, leaving a thin film on it.
Work in sections, by bringing one section to the haze, then bring the next section to haze before re-polishing the first section. Use another clean, soft cloth to polish off the haze and you should get a nice, shiny finish.
If you like, you can then use automotive polish (that includes carnuba wax) to polish it up, but I don't bother with that step. What you need to be carefule of is that Tamiya compound dries WHITE, so if you get any in panel lines or other cracks or crevices, you need to remove it once you've finished that section. Some areas (like hood grilles) might need a touch up afterwards, since I find it hard to avoid getting polish in them!
It's really hard to show the quality of shine in a photo, but here's the mustang I did: