The most notable device that they use as weapons are assimilation tubules, which introduce nanoprobes into the victim's bloodstream. The nanoprobes then take control of the victim and link them to the Hive Mind.
Drones have numerous other devices, such as claws. Some even what look like buzz saws.
As for conventional weapons, at least some drones have disruptors built into their arms (as seen in the TNG episode "Descent").
The game Star Trek Online implies they have several different types of drone. Tactical Drones have built in armaments which fire what look like Disruptor bolts. Normal drones do not have any weaponry except for a strange aility which can slow and then hold a person in place. They also attack close range using their cybernetic arm attachment, or their nanoprobe injection tubules.