Bad FL light
Just go to the hardware store and buy a new, like sized fixture. You may have a bad ballast, and the headaches of replacing one of those aren't worth the effort. Flourescent lamps are basically heaters that zing electrons between the ends (60 hz) that ionizes the gas (that contains Mercury by the way) and makes it glow. If you're burning the ends, and you have the RIGHT LAMP (size, TYPE), then the ballast is bad.
Measure the "headroom" of your old fixture (e.g., how far the lamp sticks out) and look at the mounting. It's usually 2 screws or so. Check the voltage to make sure it's 120 AC in (haven't found one not, but you never know), then cut the wires with enough slack to strip and wire nut or butt splice them together, and get it done.
If you want more work, depending on the fixture, you can pull the plug, remove the cover, read the number off the fixture, and buy a new ballast and then cut the wires (single lamp should be 7 - power, neutral, ground, two wires to each end) with enough slack to wire nut them or butt splice them on, and go to town.
If you are going to use wire nuts, make sure you stagger cut the wires, so the wire nuts don't all end up in the same place (which can make it tough to get all the wires back in the box on small boxes).
Level of work: Basic electrical - requires the ability to pull the plug, cut and strip wires, install properly sized wire nuts for the wires (or butt splices with a proper crimping tool)
Does that help?