I unfortunately got warts when I was young, and they still like to recur occasionally.
If I'm treating them myself, here's what I suggest. Get an OTC treatment with the patches. The liquid wart remover works with something like 20% salicylic acid to destroy the tissue. However, the patches use 40% salicylic acid and are much more efficient. Plus I think that liquid stuff uses acetone as a solvent, so it stinks really bad.
After a few days, you should notice that alot of the tissue is dead. Soak the wart in warm water for 5 minutes and then use a sharp knife of file to get rid of all the dead tissue. It takes a few applications, but you'll eventually get there.
Of course, if you want to do it quick then you should see a dermatologist. General Practice doctors generally don't always do a complete job on warts (atleast in my experience)
Good luck.