There are a few programs that may interfere with Garry's Mod and other Source Engine games, such as: Uninstall or exit programs that are known to cause problems
If you have Team Fortress 2 installed, you should complete steps above for it, and any other installed Source Engine game as well.
Lately Team Fortress 2 started to cause problems with Garry's Mod. You can learn more about game cache verification here Verify Team Fortress 2 and other mounted games, if any
If that doesn't work for some reason, you can do it manually: Sometimes game files might get corrupted and a file verification is necessary.
If when you start Garry's Mod the screen is black - your display settings might be wrong.
