I usually move pawn to h3, to anticipate their counterattack. But because I`m amateur, I don't really learn the opening theory, my reaction is based on my experience. Hope we`ll get better reccomendation from pro or higher ratings later 
How to play against the "Old Steinitz" Ruy Lopez?
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A 2011 book, Ruy Lopez Move by Move,
https://web.archive.org/web/20140627022042/http://www.chesscafe.com/text/hansen153.pdf
http://marshtowers.blogspot.com/2011/11/chess-reviews-190.html
devotes a paragraph to 3...d6. I do not feel up to typing all of it, but here is one line:
"White has achieved a full development, with a space advantage and a general superiority in the centre that outweighs Black's bishop pair."
BringBackTheRomantic wrote:
I use the Spanish as my main weapon as white, and especially against lower rated players in blitz I come up against 3. d6 from black. It's kind of confusing to me and probably a side line so I don't find many pointers of how to play against. Any suggestions on how to tackle this defence as white?
The standard test is to play d4 immediately and then develop quickly (as in #3). The line is supposed to be solid but passive for black.
This is Christof Sielecki's recommendation in Keep it Simple: 1.e4:
Optimissed wrote:
FrogCDE wrote:
[For the position after 1. e4 e5 2. Nf3 Nc6 3. Bb5 d6 4. d4 Bd7, this] is Christof Sielecki's recommendation in Keep it Simple: 1.e4: 5. Nc3 Nf6 ...
Don't think it's any good. 5. ed has got to be stronger than the text.
5...exd4 was considered in Ruy Lopez Move by Move:
"and White has the superior attacking chances"
I use the Spanish as my main weapon as white, and especially against lower rated players in blitz I come up against 3. d6 from black. It's kind of confusing to me and probably a side line so I don't find many pointers of how to play against. Any suggestions on how to tackle this defence as white?