Normally, that's where programming would come in. You'd find/write a game engine, and then code the game logic around that

However, you can use the Blender Game Engine to make games too. Here are a few tutorials: http://www.blender.org/education-help/tutorials/game-engine/ ; http://www.tutorialsforblender3d.com/Game_Engine/Tutorials_index.html

Another easy way to make games would be to use Syntensity. You can create maps very easily, it has built-in health and stat systems, and it does all the online hosting for you, so you don't have to figure out a way to let other people download your game.