The shut off valves under my bathroom sink have started leaking and I am not sure what to do. The sink has had a tendency to clog lately, and I am not sure if this is related or not. Are there any suggestions on how to repair the dripping valves? Please advise.

There is about three different places that one of these valves can leak, so can you explain where it is leaking?

Letmetellu correctly asked for the part of the angle stop that was leaking. From the stem? (Tighten the bonnet packing nut), from either of the compression nuts? (Snug up the nut until the leak stops.)
Your leak is not related to your slow draining lavatory. The solution is to remove the "J" bend and send a snake up into the wall. You will hit a bend about 8 inches in and from there put out about 5 or 6 more feet. Flush the line with hot water. Good luck, Tom