Taking advantage of center control?

Many gambits and openings revolve around the idea of controlling the center. We're taught as soon as we start exploring chess that the center is important. Even the most original of openings have this idea of controlling the center, be it with pawns or with pieces.

I hear it all the time: the center is the crossroads for pieces; pawns in the center are flexible and strong; you know, all the principles that really don't mean anything to someone learning chess.

My question is the following: how can I convert center control into a more concrete advantage?

As far as I understand, space in the center is more valuable then space on the flanks. I can understand that space is important, but why is it so much more valuable in the center? In the same vein, the French Defense, which is very popular, allows White to claim much central territory, yet it is described as very solid for Black.

I also am told that having 2 solid central pawns means having more square for your pieces, but I find this hard to believe. I've played a few games OTB with some opponents that have totally disregarded the center, and I didn't find any square for my pieces that might not have been there had I no pawns in the center.

For example, I've lately gotten interested in aggressive chess, and the Evans Gambit has caught my eye. It gives White a developmental advantage (which is an undisputable fact), but, more importantly I am told, it gives white 2 central pawns. Yet I don't see any way to take advantage of the center.

I've also encountered a paradox. Center control means nothing if the position is closed, right? I won't be able to move my pieces over nothing but pawns. But I can't control the center in an open position, because there are no pawns to control it.

Finally, I'd like to know how to take center control away from someone, but I think this is something I'll be able to look up.

TL;DR: I can believe that center control is important, but how can I use it to gain an advantage?