Be careful when inspecting drum brakes as there is often a lot of dust built up inside. Although they no longer use asbestos, the new materials are still harmful and you are making a big mistake if you don't wear a dust mask.
Remove the rear wheel and then with the hand-brake off, try pulling off the drum. If you are lucky it will come off easily. Normally, you end up having to tap it with a wooden mallet (no metal hammers please as this is a piece of very brittle cast iron). The rear pads have a fairly easy life and should last at least 40,000 miles. Inspect the surface of each shoe.
If the shoes are worn down to the rivets or are less than 2mm thick then get them replaced. As mentioned before, this procedure is described in my other 'jobs' page. Take this opportunity to clean the inside of the drums and remove all traces of brake dust. Make sure, there is no fluid leaking from the small cylinder shaped piston at the top of the assembly. If your drum brakes have the tendency to squeal, then try 'roughing' the surface of the shoes with some emery cloth. They can get rather polished over the years which encourages the squealing.
If you find the drum hard to get back on over the brake shoes, try squeezing the shoes together with your hands. The piston should give a bit as you do this. The drum will now be easy to get back on. Remember to pump the brakes to return the shoes to their working position.