How does gravity affect the bottom side of earth?

Gravity doesn't push things down. It attracts them to objects with a high mass. In this case, we are attracted to the center of Earth, so it doesn't matter where you are on Earth.

Gravity is pulling toward the center of the earth. Kind of like when a star collapses into a singularity forming a black hole

Hate to tell you this, but there is no bottom.  Nor is there a top.  Earth is a bit like a sphere, a ball.  It's the same all around.

Yep gravity is real, it's keeping you there sitting in that desk chair.  Otherwise, you'd be floating off to the ceiling.  So at your chair, gravity is pointing toward the center of the Earth.  Turns out, Carlos Vasquez, who lives in Ushuaia at the bottom of Argentina is sitting at his desk as well.  And gravity there is pulling him toward the center of Earth as well.  So, like you, he's not flying off to the ceiling either.

In fact wherever you go on Earth, gravity is pulling toward the ground and the center of the Earth.  And that's how gravity works; it pulls towards the center of the mass M that's creating that gravity.

By the way, there is really no downward.  But the direction gravity pulls us, towards the center of Earth, has taken on that name.  My point is that because Carlos is in the southern hemisphere of Earth, his downward, toward Earth's center, is actually pointing in a direction that's just about opposite of your downward.  In other words, what we consider to be downward depends on the direction gravity is pulling.

As to how gravity works, that's a bit more difficult.  The short answer is that no one really knows at this point.  There are several competing theories, but none has a consensus.  Simplistically, the force of gravity is generated by a gravity field g that emanates from any mass M.  Earth is our major mass, so that's why we are pulled towards its center by its gravity.