Notice how for most of the game, almost ALL your pawns were on the same color (white) squares. This is generally something to avoid as you give total control of the black squares to your opponent. Notice how both his dark squared bishop and queen were able to easily penetrate into your position and you couldn't do anything to remove them. Also his knights found nice square were your pawns couldn't attack them, because you overextended yourself. Next game, spend more time developing pieces, and (generally) leave your outside pawns alone through the opening.
How do you use a space advantage?
You spent way too many moves on pawns. You had the space advantage, but this was negated by the closed position. Your bishops had very little power while black's minor pieces were exceptionally powerful. In the opening you had a few chances to take the center before your opponent played e5 giving you a space advantage that your bishops could have used.
Some things:
Much of the time, all your pawns were on white squares, but you traded off the black squared bishop. As a result, your own bishop on g2 looked like a fat pawn that couldn't even play g2-g3. His bishop that arrived on e3 was a monster -- trading it for the rook on g1 isn't even obvious.
In general, the main advantage of more space is that your pieces are more mobile; it is easier for you to attack some weakness on one wing, let him move all his pieces over there to defend it, and then quickly move them over to the other wing. His pieces will be in each other's way and he will be unable to defend all the way over on that side.
In this game, he wasn't really cramped, partly because he had some space in the center as well, and partly because some pieces were traded. In fact, you were cramped (knight on h3, bishop without squares on g2, they're not there because they have all the board to choose from are they).
But most importantly, your pieces weren't active! You can't make use of any sort of advantage without active pieces. Look at it -- move twenty, a knight on h3, a locked in bishop on g2, and four pieces on the last rank. Development!!
The short version: don't make so many pawn moves before you've completed developing.
In this game, my goal was to secure a space advantage, particularly on the queenside. For a time, it appeared that my plan was suceeding, as my opponent was rather cramped. Ultimately, however, it failed. Did I overextend? How do I keep and use a space advantage?