I don't know what type you have, but I would squirt WD-40 into every crevice until clean, shake out all the excess you can and lube with a drop of your favorite chain lube. I have SpeedPlay X2's and that works fine for me. When in doubt, drop by your lbs and ask.
I have serviced the older style of look pedals with the spindle screws on the outside. It's easy... you just unscrew the spindle with a socket, clamp it in a vise, and pull the pedal apart. The bearings are needle and unsealed cartridge bearings. You soak in solvent, regrease, and press the whole pedal back together (I used a rubber mallet).
The newer style of look pedals require a special tool to remove the spindle. You can tell which style you have by the plastic lock ring on the inside of the spindle. If you see a splined plastic lock ring, you need the special tool. I think you can get it from aebike.com and lickbike.com
I have also serviced SPD pedals. Look pedals are much easier... spds use lots of little loose bearings and you just gotta use the special tool for those.