So it could be a number of things: the pads could need grease on the NON-braking side (i.e. the side that doesn't touch the rotors), the caliper pins could be sticking, the brake pad guide plates could be dirty and causing the pads to stick, or your caliper piston itself could be sticking slightly.
Greasing the backs of the pads is pretty self-explanatory. If your caliper pins are sticking, you'll need to remove each pin and attempt to remove any corrosion on the body of the pin that slides into the caliper. Or you could try to buy new pins if they're really bad. After the pins are clean for the most part, you would use a small file or something similar to try and clear out any corrosion within the pin holes themselves. Then, use a little bit of grease on each pin before sliding them back into place.
If your brake pad guide plates are corroded, use a flat file and gently file away the buildup on each plate until the pads can be put into place with relative ease. Apply a small amount of grease to the tips of the brake pad that sit in the guide plates as well for good measure.
Make sure to NOT get any grease on the actual braking material of the pad. If any grease gets on the braking side of the pad or the rotor be sure to wipe it off completely before reassembling.
All of these solutions are easy repairs that usually do the trick in getting rid of sticking brake pad problems. Definitely try all of these steps before looking to see if the caliper itself is starting to stick slightly and hold the pad too tightly to the rotor.