Make two objects collides and explodes

I am making an OpenGL plane shooting game. But i cannot make my bullet hits the enemy planes and explodes. Is there anyone who can teach me how? At least some algorithms will do it too.

Take it one step at a time. Can you display a plane moving across the screen?

Yes, i am able to make the enemy plane moving across the screen. And i have a player controlled plane which shoots bullet automatically. But those bullets are not able to hit the enemy plane.

This is not something that opengl can do. It is only a graphics library and what you want to do involves physics. Try PhysX, that is a good physics SDK.