I started with Bryan Vaccaro's Headspace Bowl model: which (to me) screams to be polished.

To start polishing you should work your way up through the different numbers of sanding paper starting with P400 >> P600 >> P800 >> P1000 >> P1200

 
If the surface you want to polish is quite rough you can even start with P240.
By working your way up to P1200 you are making the surface smoother every time you go up one paper.

You should use sanding paper that can be used wet (most of the times this is sanding paper that is used for sanding (spray) paint).
 

When sanding your model you should “clean” your paper with water frequently keeping it quite wet.  This will make the surface nice and smooth.

Once you have sanded your model with the P1200 paper your can clean and dry it. Once it’s dry you can start with the final round. This is polishing it with a polishing paste. This will make it shine like a mirror. I have used a car polish paste (called Commandant) and a towel.
And tatatada…. A beautiful end result 

Some tips:
- Make sure you wear latex gloves for you might also sand away some of the skin from your fingers (depending of the way your hold your paper).
- Also wear some kind of protection for your eyes and mouth.    
- You can mount sandpaper on a flexible piece of plastic to be used when sanding your model. This will help you to keep the lines in your model nice and straight.
- For the more organic models there are products (eg from 3M) that have sanding paper mounted on a sponge. This works quite well also.