Help wanted. How does gravity work?

Guest here, can someone explain to me how gravity works. I'm trying to code a quick platformer game in C++, but my program isn't working the way I wanted it to. My programming is flawless (and by that I mean it does what I want it to do), the only problem is that I'm having it do something that bastardizes physics. As you can probably guess, I've never taken a physics class before.

Gravity is a force that moves objects down at a certain rate, but how does the ground cancel out that force? Does the ground also create a force that cancels out gravity's force? 

Also, how would you go about creating a gravity program?

Newton wasn't exactly the only one who proposed an inverse square gravitation force. He was just the first to solve the differential equations to show it fit the observed orbital data to the level of accuracy at the time.