Read over the DOT's printed material on air brakes for starters. Inspect the drums for cracks, the lining for thickness, air lines for deterioration. On the front axle, pull on the slack aduster to see if the push rod travels more than one inch out of the chamber which would mean the brakes are out of adjustment on the front. Assuming the rear axle has spring brakes (a double chamber that applies your rear brakes both for stopping and for emergency or parking), a crude but quick way to check the adjustment is to look at the angle between the push rod and the slack adjuster with the parking brake applied. Less than 90 degrees would mean the rod is traveling further to apply the brakes. 90 degrees plus is what you want. This is with "S-cam" brakes. I am not sure about wedge brakes, I never drove a truck with them nor do I remember studying them.
Next would be an air leakage test. For an 87 year, I would assume that the air will leak down while sitting which may or may not mean there is a problem. Trucks will leak while sitting but still pass the leakage test. Start the truck and build the air until it stops at around 125 psi (you will hear the governor kick out). A two tank system will have dual air guages or a single guage with two needles. Both should be around 125 but may vary a few psi. Put the truck in gear and shut it off or block the wheels. Turn the key to on, allow the guages to stablize and release the parking brake. Once the air stabilizes you should not see it drop more than 2 psi in one minute. Apply the service brake (brake pedal) and the drop should be no more than 3 psi in one minute. Next, pump the pedal to drain off the air. Around 80 psi but no more than 60, you need both a visual and audible alarm for each tank. One tank may alarm before the other. Keep on pumping. Around 40psi but maybe down to 20 psi, the parking brake button will pop out as the rear brake is automatically applied. Start the engine and build the air back up. Once the governor kicks out, put the truck in gear but keep the parking brake applied. Let the clutch out enough to put a little pressure on the drive line. You are checking to see how well the parking brake holds. Lastly, release the parking brake, let the clutch out while you move forward about five miles per hour while holding the steering wheel loosely. Push in the clutch and apply the brake while checking for pulling to one side or the other. You may also want to open the air tank drains to see how much oil comes out. I would expect some.
Better yet, find someone who knows air brakes to help you out.