I didn't want to be the first to recommend oil or grease, so here goes:
I've had to do this on several stiff or grinding{!} tuners.
Remove the screw holding the round gear. You may have to gently tap the string shaft to get it out of the gear. Be careful to note the position of any washers if there are any. Lube the shaft lightly (grease or oil) and wipe off the excess. Do the same with the round gear.
Using a toothpick, put a tiny amount of lube on the tuner bracket's bearing points and on the worm gear. You don't want any to drip or otherwise get onto the wood. Spin the tuner knob around a few times while wiping off the excess.
As you reassemble, test the string shaft by spinning it in place with your fingers to make sure it turns smoothly. Then install the washer and round gear/screw. Again, wipe off any residual lube.
The whole assembly should now turn smoothly. If not, it just may be a bad tuner.