Control of the center

I have been playing chess for a while and find myself slowly improving. As a chess newbie, I learned that center control is extremely important and often leads to a small advantage.

Now as a roughly 2200 player, I find that in the majority of games (especially white) I often have a dominating center with +0.5 to +1 advantage (as I suspect from having the center). However trying to capitalize on this advantage feels incredibly difficult and most of my games, in my opinion, are not decided by having a dominant center.

Having a center, (and in a lesser way, having a space advantage) are the two advantages that I have the most trouble realizing. My theory is that having a dominant center does lead to a majority (or comprise of at least a large fraction) of my wins, however it is not immediately obvious that other forms of advantage eg. material/weak king/passed pawn stem from said advantage, despite originating from it.

If any strong player could tell me (if any), a concrete idea or explanation that leads from having a large center provides, as well as general directions or plans to play when I do control the center, it would be greatly appreciated.