One known method is to play Qe2, Nd1, Ne3 (kicking the Bishop back to h5), Rfe1, Nf1, Ng3 (kicking the Bishop back to g4) and finally h3.
This uses up a lot of time, but Black also loses several moves with the Bishop... and your Knight is arguably better placed on g3 anyway.
Another possibility is to play the b1-Knight to d2 (instead of c3) from where it can reach g3 in two more moves instead of four.
One known method is to play Qe2, Nd1, Ne3 (kicking the Bishop back to h5), Rfe1, Nf1, Ng3 (kicking the Bishop back to g4) and finally h3.
This uses up a lot of time, but Black also loses several moves with the Bishop... and your Knight is arguably better placed on g3 anyway.
Another possibility is to play the b1-Knight to d2 (instead of c3) from where it can reach g3 in two more moves instead of four.
That's perfect, blueemu. You are awesome. 
It's definitely a lot of work to kick that Bishop away. Any idea if it's just better to move the Queen and allow for doubled pawns? I wonder about that too. But I generally hate doubled pawns - especially on the Kingside, where my King safety is concerned.
I wouldn't allow the doubled f-Pawns (after O-O) unless the e-Pawn was still on e3. The Pawn formation e4/f3/f2 is much weaker than e3/f3/f2.
The most serious weakness involved in doubled Pawns is the loss of "collective mobility" of the whole group of Pawns... and this is much worse if there are no duos (no Pawns side-by-side) in the group.
This is probably obvious to most, but why not h3?
After h3 and Bh5... then what? How do you break the pin without totally disrupting your own castled position with g4?
True....I would usually play G4 which is not ideal, but it does leave the bishop trapped in the corner, and I can then play Ne5, NxG3 leaving him doubled pawns on the kingside...Haven't really been punished for this but I imagine at the higher levels people will take advantage of kingside pawns being pushed forward.
Youre worrying about something that doesnt need to be worried about. Play h3, and if black takes, your queen is developed, and if black doesnt take then play g4. If black castles king side you have the start of an attack.
That advice can work if Black has castled K-side before White does. In the game shown above, exactly the opposite had happened... White was castled K-side and Black still had choices of where to put his King.
In a situation like that... White has O-O and Black not... Black can even meet h3 with h5 (instead of Bh5) in some cases.
Example:
h3 is the move or Qc2
Or try the KIA (King's Indian Attack); uses the b1 N to go to d2 for support for the N at f3:
You could play Qe2 Qe3 and move the knight.
But it is pretty slow.
The usual Lopez thing is Rf1-e1, Nb1-d2-f1-g3 and h3.
I am not sure the Ruy is recommended at your level. Not that it isn't good, but the ideas and move order considerations behind it are subtle, so you will probably miss them; better play something that is a good teacher.
You missed checkmate on move 19. Rook to H8#
Don't beat yourself up from all these comments on what you missed, etc.; most of us miss all kinds of opportunities and it takes a while to see some of these. You are doing the right thing by going over your games and seeing which moves could have been better and even what your opponent could have done better. Start doing some chess puzzles (solve for mate in 3 etc) along with the game analysis, it will sharpen up your chess vision.
First, let me say that I'm still learning this game and am not very good. So, please don't laugh!!
YES, there are many blunders in this game probably (especially when I left my Rook hanging after an exchange). Both sides blundered a bit actually. Nevertheless, I'm simply interested in knowing how I can alleviate an annoying pin that occurs a good deal of times while playing the Ruy Lopez as WHITE. Here is the game:
I get my knight pinned on MOVE #5, which becomes annoying for me, but for which I didn't have a plan to un-pin (spelling??) during this Blitz game. I won the game still, but still would love to know some unpinning techniques. Thanks very much!
(p.s., I forgot to add that I know I can move my Queen, but then BLACK could take my Knight and double my pawns. So, I'm wondering if there is a way to unpin AND not get doubled pawns.)