That's something you're born with I'm afraid, although you can encourage it. IQ will help you visualize the board better. I recommend this program...
https://www.bulletproofexec.com/how-to-add-2-75-iq-points-per-hour-of-training/
Something you have to remember though, is that memory is not anywhere near as important as tactics are. I hope I was of some help. 
I can't remember if they do
.....wait!, what thread is this?
I don't know what's cheesier. The idea that IQ helps you visualize or that those exercises are meaningful to actual intelligence.
As far as I know it's never taught directly. It doesn't need to be. Every time you play a game or try to work out a position you're practicing visualization. Average people will have difficulty visualizing a few simple moves when they begin. Over time it becomes easy and what limits you is not visualization, but judging the future positions correctly.
As for remembering games, after you've learned a lot, groups of pieces (like pawn structure or the castled king's quadrant) are remembered as chunks. Instead of remembering 5 individual pieces or moves you remember groups of pieces or series of moves. If you give a grandmaster a position or game to memorize that looks nothing like an actual game (i.e. nonsense moves or illegal positions), they do no better than a non chess player when trying to remember it (this has been studied).
I myself will remember a tournament game I played days later even if I haven't reviewed it yet. But if I play a beginner who makes nonsense moves I usually can't recall the whole game immediately after playing it.
Actually now that I'm typing this, I recall a good recent example with Carlsen. Phenomenal memory for chess by the way. There was a chess trivia contest (with questions like showing a historical position and naming the players who played the game). Most players were grandmasters (older than Carlsen). Carlsen won the trivia haha.
Anyway, what I remembered was that in simultaneous blindfold clock simul, Carlsen only lost track of the position in the game where his opponent made a bunch of random moves, shuffling back and forth. He had the easiest time against the player who played a normal opening (which of course led into a recognizable middlegame).
@24:20
The player who played the worst was the most difficult lol :)
https://www.youtube.com/watch?v=lqmzadHNSLs
This is one of my pet peeves, since I believe there's a huge lack of instruction in that area, as well as a huge lack of research.
For example, I'm currently a chess instructor for elementary school after-school classes, and nowhere in all our months of training and forced watching of videos was there even a mention of how to look ahead, much less blindfold chess: only openings, heuristics, famous games, endgames, etc. The same with one tournament director who used to help me out: he was great with everything but when I mentioned I couldn't see far enough ahead regarding one tactic he just said, "I can't help you there."
If I ever get enough free time I plan to work on an entire system, theory, visualization rating, and computer program to help everyone out, especially myself, but it's quite possible I'll never get the time.
http://www.chess.com/forum/view/general/how-do-you-practice-chess-visualization
It's odd to me because visualization isn't some hidden secondary skill that's hard to find ways to practice. You can practice it directly any number of ways... and often do simply by playing games and solving puzzles, even if you don't realize it.
The same with blindfold games... simply play blindfold games with the goal of going further into the game before you lose track of the position. You'll likely stumble onto Tisdall's stepping stone method on your own.
Tisdall has some tips in his book
http://www.amazon.com/Improve-Your-Chess-Now-Tisdall/dp/1857441567
Hi, I've a quick question to those of you who may have taken or are simply familiar with formal, structured chess instruction. What methods, if any, do chess teachers use to train their students' ability to remember chess games, positions, or just to visualize without looking at the board? As someone who has begun to study chess at age 30 as a hobby I am curious how this might have been taught.