My instinct suggests "replace washer". This sounds simple enough, but if you couldn't guess that one, then perhaps the inevitable complications you'd encouter when doing this yourself may be beyond you.
However, at the very least, you should (now) be better armed to instruct a plumber/handy-man on how to sort it for you without charging you an arm and a leg.
If you still fancy having a go yourself, the instructions on this page seem to be comprehensive:
http://www.diydata.com/problem/taps/washer_replace.htm
Chris Murphy
September 2006