Hi Adam - Great Electrical Repair Question!
First of all - one thing that will burn out a ballast is when the lamps are not changed when they start to flicker and get black at the ends. If this happens to both lamps chances are you will need to change the ballast, and unfortunately the ballast is much more expensive than just replacing the lamps.
Typically the average life span for lamps is about two years, depending on how often you turn the lights on and off, which will decrease the life of the lamp.
Replacing the ballast is really not very hard at all. Be very careful that the new ballast is the right replacement for your fixture lamps type and length and that the watts are comparable to the watts of your lamps. The first thing before replacing the ballast is to never change the ballast if the switch or power is on or you could get a nasty shock. If you have the correct replacement ballast the wire colors will match and if there are two wires of the same color it will not matter how you match them up
You will need a pair of wire strippers for the smaller gauge wire and small wire connectors to make good tight splices. One pair of wires will typically be black and white which are for the 120 volt power coming in from your switch, the other wires go to the sockets for the lamps. Be aware that the wires that attach to the sockets can sometimes become disconnected but can be inserted back into their termination hole. If a socket is damaged they can usually be replaced. These sockets are called tombstones by trade name because of their shape and can be found at any good hardware store or wholesale electrical supply house. While inside the fixture, make sure that it has a ground wire that is attached to the frame of the fixture. The Lack of a attached ground wire can prevent your fixture from starting, especially if you are replacing a magnetic ballast.