(If you clutch is actually working okay, you prolly don't need to bleed it) But if not, it's basically the same concept as bleeding brakes. Of course you will need an assistant to pump the clutch pedal. Be sure to keep enough fluid in the master cylinder. If the fluid level is low and the pedal is pressed, you will have air in the system and be right back where you started.

One thing I am still puzzled by is why it's leaking from this part of the cap? I know in my master cylinder (92 P/U) there is a plastic floater that floats on top of the fluid. But I'm not sure what purpose it serves.

Did you see what happens with the fluid when the clutch is pressed and released with the cap off?