Assuming the drainage lines were piped properly, tubs and showers usually have hair as the main cause of their stoppages. Physical removal of hair is best. The regular use of a safe enzyme based drain cleaner product such as BioClean can help prevent slow drains and stoppages.
The most often clogged drain is the kitchen sink. Kitchen sink stoppages are usually caused by liquid fats, emulsified by warm soapy dishwater and then carried through the drainpipes. As the water cools, it proceeds down the drain and leaves the fatty deposits along the piping. A film of grease forms on the pipe wall and so on. Coffee grounds, egg shells, etc add to this accumulation layer until the pipe becomes impassible.
We recommend that you pour excess grease into a tin can, not down the sink drain. When using a garbage disposal, always let sufficient cold water run to carry the particles down and into the main line to prevent buildup in the smaller waste lines.
The Plunger... A Plumber's Best Friend
In the event of a total stoppage, you should have a plunger (with a large rubber suction cup with a wooden handle). Cup it tightly over the drain and plunge it vigorously several times. It is best to try to use the suction cycle rather than the pressure cycle of the plunger. What we mean is that one "should" push slowly, make sure the plunger is sealed to the drain and then pull quickly on the plunger. This tends to loosen rather than pack down the stoppage. If it is a double drain sink, make sure you seal the other drain so water will not splash out into the other bowl or on you. Drain piping can also be cleaned by removing the J-bend on the trap below the fixture.