How to fix gears on a Kilimanjaro bike
You need to read about derailleur adjustments. The first thing to do is check that the rear derailleur is not bent. If it is, you need to unbend it.

Once that has been determined, you can read up on rear derailleur adjustments and front derailleur adjustments. I'm including cable tension as a derailleur adjustment. 

Other problems may be cable friction (replace the cables) or the shifter pawls not catching (replace the shifters). But start with the derailleurs.