From what I understand, the gravity on the surface of a planet is determined by it's mass and it's size. A really large planet might have a lower gravity if it has little mass or because the surface is so far from the center of the planet.

(please tell me if I have this wrong)

How is the mass of a planet (other than the one we are currently on) determined?

When you are talking about planets and gravity, density is a good word to throw in there, because a planet could be big, but only comprised of gasses, so it would not have much gravity,
or the same size planet could be all lead, and have a lot of gravity.

the gravity a planet can be estimated by its size and what materials it is primarily comprised of.
though i dont know how it is actually done, but if you know those two things you could find it out.

it could also be found by sattelites orbiting the planet with instruments, or the effect the planet has on nearby objects.

You've got it right and so does BibC14, but here is a site with more detail about GRAVITY
and More gravity