There are a lot of great detailed explanations here. I'll just provide the simplest one feasible.

In low drag environments, the relationship between gravitational acceleration, time and distance are pretty clear: D = 0.5at^2.

All you need is an object to drop from rest, an object of known length (ie yardstick), and a stopwatch. Once you have time and distance, solving for gravitational acceleration becomes pretty straightforward.

Edit (in case you cant travel to or close to said planet): Alternatively, if one is unable to test within the gravitational field, the centripetal acceleration relationship also works: a = v^2 / r.

One would simply identify an orbiting satellite, mark it's orbiting velocity v and the orbiting radius, r. Gravitational acceleration can be calculated by solving for a. If orbiting radius is unknown, one could simply use the alternate formula: a = 2piv/T, where v is orbiting velocity and T is the amount of time needed to complete one full revolution.