Cables for my rear gears do not work
If the shifter does not move the derailleur at all, then either:


A cable housing has come free from the shifter unit, frame boss or derailleur 
A cable end has detached from the shifter
A cable end has detached from the derailleur
The cable has broken (least likely)


Basic things you can do to find the problem:


Find an exposed bit of cable (the inner silver cable, not the black housing) on the frame somewhere. It should be taught and not loose.
Inspect the shifter cable run from the shifter to the derailleur, make sure the cable housing is inserted into the shifter unit, all frame bosses and the derailleur.
Find an exposed bit of cable near the derailleur, grab hold if it (using pliers will help), put a little tension on it and operate the shifter. If the cable moves it's attached to the shifter.


If the cable is moving near the derailleur when the shifter is operated, check the cable is attached to the derailleur.