The process of repairing a dryer depends on the nature of the problem; dryers that stop working completely likely have a problem with their electrical connection, a fuse or the door switch. Little to no cooling can be caused by a damaged heating element or ventilation.
If the dryer won't turn on or spin, it's important to ensure the electrical cord is connected and undamaged. Dryer fuses are generally easy to access, and a quick replacement can get the dryer running again, although multiple blown fuses likely indicate an electrical problem within the dryer or with the outlet the dryer is connected to. Dryers are designed to run only when the door is closed, and the dryer might turn on if the switch is manually depressed.
If the dryer spins, determining whether the sides of the unit heat up or not can help reveal the nature of the problem. Warm sides mean the heating element is working in electrical dryers or that gas is burning in gas units. If the clothes aren't warming up or drying, the fan that blows hot air into the dryer may be faulty. The exhaust may be blocked as well. If the unit can't vent properly, moisture can't be removed from the system. If the dryer stays cool, the problem likely lies with the heating element in electrical dryers or the gas line or ignition system in gas dryers.