I often get asked this question, so have tried to put it into as simplest steps as possible.
Here are my nails 2 1/2 weeks after I put gels on them
Step 1:
Use a nail file to buff over the top layer of the gel, this breaks the seal of the gel and allows the acetone to soak into the nail. 
Step 2:
I next use already prepared pads soaked in acetone which I wrap around the nail. You can buy pads or you can make your own by cutting up pieces of cotton wool and normal kitchen foil. 
Step 3: 
Leave on for 10-15 minutes. Remove the foil, and gently scrape off the gel. Use a buffer to gently buff the nails. 
Step 4: 
I would now recommend using cuticle oil and hand cream to help condition your nails. It would also be a good idea to use a nail strengthening product such as O.P.I. Nail envy.