Yours is a common problem. The normal physiological response when something is put into the mouth is for the salivary glads to become active. This happens to some of us more than others and we shall be known as "the droolers".
Seriously, what I have found that helps me is:
-Swallow as much saliva as possible before starting to play
-During rests and breaks inhale sharply through the mouthpiece to draw the water back "to whence it came"
-During breaks remove the reed from the mouthpiece and pull a clarinet "hanky" through the neck and mouthpiece a few times
-"polish" the back of the reed by rubbing it over the inside cover of a music book placed on a perfectly flat surface. Rub with the grain lightly at first and then harder. Finally you will hear a clicking sound when you rub. The back of the reed becomes shiny and the water droplets will roll off like when you wax your car. This procedure can be repeated every few days. An added bonus is that your reeds with play better and last longer too.
John