I think really the biggest part of mindgames is having the right mindset (much like the first post states, but kinda shortened up really)
1st thing going into any match is being confident in yourself, so long as you tell yourself you are worse you will be worse. really that simple. anyone can beat anyone any day given the right mindset, no thanks to miracles.
2nd thing is keeping your cool at all times. you cant lose it all because someone just did some crazy technical combo on you and let it get to you. many times in videos I have noticed people come back on their 2nd to last and last stock and take the win because they begin to catch onto their opponent. this leads into the 3rd thing...
3rd is patience. you gotta have the patience to notice what your opponent is doing. I know personally I will always try to find something that works on a particular opponent and do it over and over and over again. if it works and they aren't countering it, do it. (this part I believe is what sets apart pros from everyone else, they catch on much quicker and are able to exploit weaknesses much faster than the average player) should you find your opponent doing this to you, stop them, counter their counter. sirlin explains this well in his rant on how scrubs will always be scrubs so long as they keep their mindset (when he talks about chain grabbing)
from what I have seen in 2d fighters as well, pressure is key in many cases (if not all). if you can keep the pressure on and make the opponent lose their patience, this in itself is a mindgame, and one of the best. that why it is so important that you do something that may be looked down upon by others.
Taunting your opponent (for the most part) is one of the best things you can do when you kill them. give them no rest, no break from the mental pressure, even in their death. make them lose their patience, you will always have the upper hand.
granted taunting only works should you have the mental capacity to get flamed to death during, before, and possibly after the match, because it really is frowned upon to rag on your opponent. I generally dont do it unless I know it could be the difference between a win and a loss, and due to me sucking really I hardly try to piss others off during a match.
but, should it ever become the difference between $2k and $500 for me, I am sure as hell going to be making fun of my opponent every chance I get.