mixer tap dripping from spout?

Isolate the water first.
I've know someone take a tap apart and said something like Oh I'm wet! may be I wasn't hearing properly as it seemed a longer mouthfull.

When cap removed you are seeing the obvious brass nut typicaly limed in no doubt or over tightened.
Good fit spanner and get someone else to hold the other tap a a precaution and give the spanner a sharp tap anti clockwise the shock usually releases the tap you may have to replace the whole valve / washer carrier if its not the old black washer type.
On replacing smear vaselene(petrolium jelly) around the tap body thread to help prevent lime build up tighten hand tigh an approx 1/3 - 1/3rd touch with spanner. Fit tap cap try turning top on and off make sure the body is tight enough it doesn't come lose when turning the tap cap

bob
March 2013