As White you have a major advantage. You have the 'initiative' and you can dictate the whole game since black always has to play catchup. So, as an opening move you should use that advantage to sieze territory and restrict blacks movement. Most chess experts think that if you're going to do that with your e pawn you should move e4. That really starts a good attack and controls d5 and f5 squares off the bat. e3 is ok if you're going to follow up with d4, but overall kind of tenative.

I follow up immediately with d5 to control the center a bit more.

This is good. You are counter attacking my pawn and now I have to defend

this is good. You are now trying to reassert control over the center but note that you are now behind in the initiative somewhat. If you had moved d4 from the start you would have owned those squares right off the bat

it's always good to get your kings bishop out and about early (so you can have room to castle and also to restrict blacks development), but this isn't a great spot for the bishop (as you will see in a couple of moves)

now. I aim to attack your d4 pawn since you don't have it backed up with the night on the f3 square. So exd4, exd4:Nxd4 puts me in a really good position and gives me control over the center of the board and pressures you on your 2nd rank

?? bringing out your N normally would have been good here since it would make me reconsider my attack, but you made a crucial mistake.

fork. You just lost a piece.

choosing to loose the N over the B was good since bishops are a tiny bit more valued than knights.

? this was a bad move for 2 reasons. First, you have doubled your pawns. pawns in the same column are generally a bad thing since they restrict movement of each other somewhat. Secondly you ruined your pawn wall for your castled defense. A beter move would have been Bxg3 which would have then attacked d5