What to do with space? I sometimes find that after an opening, I have created &quot;space&quot; for myself, and control most of the board. But then I'm not sure what to do next.
For instance (0 6 time control on Lichess, me 1560 vs 1400):
[FEN &quot;&quot;]
[StartPly &quot;25&quot;]

1. d4 e6 2. c4 c6 3. Nc3 d5 { D31 Semi-Slav Defense: Accelerated Move Order } 4. c5 Bd7 5. Nf3 Nf6 6. Bg5 Be7 7. Bxf6 Bxf6 8. e4 dxe4 9. Nxe4 Be7 10. Bd3 b6 11. b4 bxc5 12. bxc5 Bc8 13. Qd2 Ba6 14. Bxa6 Nxa6 15. O-O Qc7 16. Qd3 Nb8 17. Nfg5 Nd7 18. Nf3 Rb8 19. Neg5 h6 20. Ne4 O-O 21. Rab1 Rxb1 22. Rxb1 Rb8 23. Rxb8+ Qxb8 24. Qc2 Qb5 25. h3 Nf6 26. Nd6 Bxd6 27. cxd6 Qd5 28. Qc5 Qxc5 29. dxc5 Nd7 30. Nd4 Kf8 31. Nxc6 Nxc5 32. Nxa7 Ke8 33. Nb5 Kd7 34. Kf1 Nb7 35. Ke2 Nxd6 36. Nxd6 Kxd6 37. Kd3 Kc5 38. Kc3 Kb5 39. Kb3 f6 40. a4+ Ka5 41. f3 g6 42. Kc4 Kxa4 43. Kc5 e5 44. Kd5 Kb4 45. Ke6 f5 46. Kxe5 Kc5 47. Kf6 g5 48. Kxf5 Kd5 49. Kg6 Ke5 50. Kxh6 Kf4 51. Kh5 Kg3 52. Kxg5 Kxg2 53. f4 Kxh3 54. f5 { Black resigns. } 1-0

I'm equal on material, ahead on development, and I control much more of the board.
How do I convert these advantages into something concrete?
Having a space advantage means you have more room to navigate your pieces.
Space may allow you to attack on both sides of the board, or attack on one side then switch to the other;  the cramped defender simple can't navigate as well.
You may be able to dominate an open file as it is easier for you to double or triple heavy pieces.
In late middlegame to endgame situations your king can get further up the board.
In your specific game black has a lot of weak squares and is behind in development as well as space disadvantaged.  Your play needs to consider other fundamental elements.  First after 13...Ba6 you shouldn't waste time with 14.Bxa6 which after Nxa6 allows Nc7-d5 with occupation of an outpost.  But rather just continue development with 14.0-0
In the game black continued to play horribly with 15...Qc7 and after 16.Qd3 Nb8 you have various options.  Doubling rooks on the b-file and penetrating the 7th rank will be crushing.  Consider the rook lift Rb1-b3 -- if Black castles trying to get his h8 rook in the fight, the b3 rook can swing to the kingside.
You can also think about occupying d6 with a knight (Ne5-c4-d6).
Wasting time with Ng5 and back like you did is not because you don't know what to do with space, but rather you don't know what to do with your pieces in general.
Target weak squares, coordinate, and invade!