Ruy Lopez exchange variation

The variation in your game is not the "Exchange Variation," although you did eventually exchange your Bishop on c6. When people talk about the Exchange Variation, they specifically mean 1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Bxc6. When Black plays 3...d6, as in your game, it's called the Steinitz Variation. And in the Steinitz Variation, White almost always plays 4.d4, although your move is also reasonable. Once again 5.d4 is probably your best; there's really no need to spend the time preparing d4 when you can just play it.

In fact, Black would have had a slightly cramped, but reasonably solid position if he had just played 7...O-O. By exchanging, he gave you the big center of your dreams for free. 10...Bb5 looks wrong; doesn't it just let you develop your Nc3 with a gain of time? But I don't think 14.axb5 and 15.Rxa8 is the right way for you to go. When you have a big space advantage, it's usually wrong to exchange pieces. I think I would prefer something like 14.Qd3 and 15.Bxd2, completing your development, connecting your rooks, and just suffocating Black. Don't get me wrong though, you have a nice advantage the way you played it too.

Black gave you a great d5 outpost with 17...cxd5 and then committed suicide with 19...Be5 (after 19....Bd8 he is quite a bit worse, but there's plenty of fight left.) You should have ended the game right there with 20.Nxe5 dxe5 21.Ne7+ picking up the Bd7 for a free piece. After 20.Nh2? Be6 you're back to square one, with a fairly even game. or at least you would have been after 21...Bxd5 22.exd5 Bc3

You missed another game winner with 26.Ng6+ If 26...hxg6 27.Qh4+ Kg8 28.fxg6 will force mate. Luckily, Black played 26...Rxf5 and gave you another chance to put him away.  You missed 29.Nh8 mate! But it wasn't easy to see and Black was dead in any case.