As a beginner I've been studying openings for center control. I am having a hard time finding the next lessons and steps when I actually have the upper hand in the center. Now I realise I don't actually know what to do when you have the center. How do I learn the next steps and what should I learn to improve in this area?
Once you control the center attack the enemy king and give checkmate!
However it's much easier said than done.
Normally there are two ways you can win control of the center and how you go about trying to win in each case is different.
1) You both fought for the center by moving pawns there but you managed to swap off or divert his pawn or pawns and now you control the center. Classically this could be via a gambit like King's Gambit (you played f4 on your second move to divert his e5 pawn to f4), Scotch Gambit or Goring Gambit (d4 on the second move followed by c3) or Morra Gambit in the Sicilian.
Because the center is open for your pieces you can move your pieces quickly towards the enemy king and go for checkmate. A good place to start studying here would be the romantic players of the 19th century like Anderson and Morphy.
2) Your opponent didn't really try and fight for the center with pawns instead he only moved some pawns to the 3rd rank, developed his pieces behind this pawn shell and aimed one or two of his pieces at the center by, for instance, fianchettoing his bishops. These would be openings like the Reti for white and the Pirc, Hedgehog and Hippopotamus for black.
The problem here is that because your opponent didn't weaken his position by fighting for the center with pawns he probably has a very strong defensive position which you need to try and break down. You will need to build up slowly with your pieces before trying to open his position with pushing one or more pawns into his position to break it open. Your opponent is hoping that you will create weaknesses in your own position when you do this and he can launch a counterstrike against your over-extended position. He could be right!
A good place to start here would be the games of the hypermoderns from the early part of the 20th century, players like Reti and Tartakower.