Begin by getting the wheel off the ground.  Then loosen the axle fastener (nut or bolt) so that it's finger tight. Now, while rotating the wheel in a forward direction apply the brake quickly and firmly and hold it while tightening the axle fastener.  Often a helping hand is needed as two just aren't enough. 

This effectively centers the brake backing plate and shoes in the drum opening and usually allows good contact between shoes and drum.  The axle hole in the backing plate is usually just a bit larger than the axle diameter, allowing this to occur during the process.

I've used this technique on older British and German bikes over the years, and most recently on my Suzuki Boulevard M50 -- it definitely helped a bit.  I'd suggest doing this everytime you remove or replace a tire or adjust a chain. 

Ray Nielsen, in Minneapolis and sitting out the current snowstorm.

Here's some additional info for consideration by all of us with old style drum brakes.

Anybody ever see an old drum drilled for venting or lightening like discs are drilled? Me neither. I wonder why that was never tried?

Its also possible to scuff the drum surface with some emory paper. This is done conveniently anytime the wheel is off.  The emory paper will cut the glaze on the pad if there is any. Look at the pad closely to see if it is making contact across the whole arc. New or re-lined pads need to be bedded/seated to the drum. It may take a lot of light, repeted stops for the pads to conform to the drum and maximum braking results. An old bike with a modern tire and a good double leading shoe brake is capable of stoppies.

Another trick is to cut a narrow groove into the brake pad/lining with a hacksaw. About half way through the pad is enough. The cut should be on a diagonal and not square across the pad. Carefully consider which way the wheel rotates and cut the groove so that water is pushed toward the backing plate and not deeper into the drum. The idea is that the pads will wipe water out of the wet brake quickly and work faster. Some solid discs have pads without a wear groove cut into it relying on a paint stripe to tell the rider that the pad needs replacement. Some of these brakes are notorious for zero drag when wet and sudden grab when the dry part comes around. Some riders hacksaw a groove into the pad and declare that the feel of the initial application is much improved.

Some bikes have vented brakes and will ship water in heavy rains. My antique triumph is such a bike and I carry duct tape to block the vent if caught in a continuous or frequent spell of heavy rain.

Some bikes with wet brakes, disc and drum, will seem to have zero braking and then grab suddenly. When the brakes are applied, it takes a turn or two to get the water wiped off. When the dry part comes around the brakes grab.

When rain riding or the brakes are wet for some reason, I like to leave an extra second of following distance just to account for the drying brakes. Braking lightly to dry the brake and getting a feel of drag before applying more pressure keeps me from overbraking in the rain. 

nobody rides half as well as they know how.