Starcraft 2407

If you're not a do-it-yourselfer, bring the trailer to a dealer and look at them. If you are confident and capable of Jack on one side, remove the wheel and see if there is a brake drum. If yes, then you have electric brakes. You must also, if the brakes are present, the proper electrical connector to fit the wiring harness of your car.

There are only two types of trailer brakes.
Hydraulic brake booster with a tank on the tongue, and electric brakes.
If there is no mechanism to slide on the arrow in the trailer, you have electric brakes.

ADDED:
Well, there are air brakes too, but this only applies if you drive a big bench.