you will have one cable to each brake drum.
what i would do:
lift the back wheels off the ground. spin each wheel to see if it's dragging more than the other. this may be difficult if you have a limited slip.
remove the wheels and drums. look for any abnormal wear on the shoes, and the drums. also check for heat cracking.
check each brake cable, probably easiest to disconnect the two cables and give each one a pull to make sure they move freely. don't pull to hard if you have the drums off and the drum end still connected, peices may fly!
take a garden hose and rinse the brake dust out of the brake assembly, and the drum. let it air dry, they give them a spray with brake parts cleaner a wipe them down to remove any remaining residue.
check the adjustment (assuming you don't have to replace parts).
re assemble and test drive it.
brake dust and water basicly turn into glue! this can really be a problem if you back a boat trailer into the water, and go in up to the drums. the next place you park, the brakes may sieze on when the water starts to dry up.