A couple of things to try would be:
Reset the PRAM
Restart your Mac
As soon as you press the power button to turn it back on, hold the
⌘ + ⌥ + P + R keys until you hear the startup chime twice
Reset the SMC
Shut down your Mac
Remove the battery and unplug the power cable
Hold down the power button for 10 seconds and then let go
Restart your Mac normally
These steps may not resolve your issue, but it's worth a shot. If they do no resolve the issue, it is likely related to the inverter board, which sends power to your display backlight. It's relatively common in this model MacBook.
It shouldn't be to expensive to repair, but I would not recommend doing it yourself. It's taken me hours to do that repair, and that's in an Apple Store with all the right tools, Apple Technician Guides and the proper training.