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?

For the purposes of coding, either apply a force to the object equal to the object's mass times the gravitational constant you choose, or if you're merely looking for the acceleration, just change the velocity of said object in accordance with the gravitational constant.  Remember: Force = Mass x Acceleration