Instructions
Compare the game's system requirements with the hardware on your computer. If your computer does not meet the minimum system requirements, your computer will likely fail at even starting the game's main menu.
Upgrade the drivers on your video card. Drivers are updates for your hardware that increase the efficiency and compatibility of the object with other programs. Updating your card can improve its compatibility with programs, both new and old, and resolve many common hardware problems.
Reinstall the game. Files can become corrupted for a variety of reasons, including in the installation process, so reinstalling "X-Com: Apocalypse" can give you a fresh batch of files to work from when trying to run the game. Any saved games you have will be erased unless you back them up, so this is typically a measure of last resort, even though it usually effective.