What kind of bike? A Chain tensioner is used normally on a multi-speed bike that has been converted to a single speed. If your bike is a multi speed and you have the problems you have described, you may need a new chain and freewheel or cassete (rear wheel gears) and or a chain-ring or two (front gears). This work can be done by the home mechanic. If you want to learn, check out Sheldon Brown and Park Tools.
http://www.sheldonbrown.com/
http://www.parktool.com/repair/byregion.asp