Here is what I use:
Acetone, small bowl, angled brush
This is a close up of the brush that I use. It is just a flat angled brush.
So this is yesterdays mani before I cleaned it up. You can see the polish on my skin and cuticles in these two pictures:
Ok here is how I do it:
Step 1: fill the bowl just a little with acetone and dip your brush in it. I usually dab the brush on a paper towel after dipping it, otherwise you will flood your nail with acetone and take off more polish than you want.
Step 2: Clean the polish from one side of the nail, then the cuticle, then the other side. Or in any order you would like, it doesn't really matter. Make sure you are using a nice sweeping motion and that you are not putting too much pressure on the brush. It does not take very much pressure to get the polish off.
Here is a picture comparing the cleaned nail to the uncleaned nails. See what a difference it makes:
Here is the before and after pictures:
Before Clean up
I hope this was helpful!