1) Find the biggest game database you can. Filter for checkmates.
2) Sort resulting games by number of moves, least on top.
3) Go through games one at a time in order, revealing one move at a time, blindfolded. After each move, try to find the impending checkmate.
As you go through these games, your abilities should increase and the games should gradually get longer.
A better "blindfold" interface would just be removing the chessboard and replacing it with a simple textbox to enter the notation :)
Shouldn't be too hard to implement at all if they wanted to.
Edit: Not that what they already have isn't an improvement over the old blindfold interface ;)
I played some blindfold games today at 3, 5, and 10 minute time control, against players above 1500 blitz. I won 2 in the 5 minute bracket and drew 1, and I think I mustve lost like 4-8 others I cant remember how many. Anyways I got good at blindfold by doing tactics without moving the pieces so many times that I could visualize very deeply the obvious responses and tactics in the position and somewhat deeply the really complicated stuff. That and I played a lot of blitz games using similar openings to the point I just knew what certain things looked like. The only trouble I have playing blindfold is the endgame (with actual blindfolds more than the chess.com interface), too much empty space!
Try reading chess games without using a board. When you get just about as far as you think you can go, really concentrate on that position and write down where every piece and pawn is. Then see if you can go further. If you can't, set up the position, see if you were right, and go on from there.
Practice visualizing complete games, and you will begin be able to play blindfold chess. I believe that just about anyone can learn to do this, but it requires patience.
There's an expert on another site who play all his blitz and bullet games blindfold. His rating is very impressive, but it mostly comes down to practice.
If you can't visualize the entire board (like me), then do what I do. I know in principle where each piece is, and I refresh every so often to myself where they are. Then, if I'm considering some move (like Bg5 for example), I'll go through all of mine and his pieces, making sure there is nothing in the way.
I know it sounds a little hokey, but the piecewise board remembering is the only thing that's worked for me.
That's what I have to do. No idea if it's bad or good or easier or harder. Every so often I have to refresh where each piece is. If I get lazy and don't refresh often enough it's sometimes comical... crap he has a bishop somewhere... where the hell is that bishop... wait was it light square or dark square... uh oh (lol).
Same as you Ozzie, atleast when a board isnt sitting blank right in front of me like the chess.com interface xD
"Become blind."
If you were really blind, why would you need a blindfold?
To prove to people you can play blindfold. Otherwise, yes, it would make no difference 
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I think I have the skills to play Blindfold. I've already beat a freind who's 1300 blindfolded while he looked at the board
i can play blind fold chess till only maximum 10 moves maybe i wish i can know more.
This is a helpful thread. I need to visualize so I can evaluate.
JUst won my first game of blindfold chess: White to play and win blindfold.
I tried, and it was very amazing! Though it was hard. But to play blindfold chess, you need to learn coordinates.
Get a book of games and two chess boards (or a chess board and a computer program).
Play out 5 moves for each side in your brain.
Use one chess board and set up the position. Do not make the moves, just put the pieces where they belong. Try putting all the knights on their squares, all the bishops, all the rooks, etc.
Play through the moves on the other board (or computer) and compare the results.
If you can visualize 5 moves easily, go to 6 moves, then 7 and so forth.
Start asking yourself questions about the position "What squares do the dark squared bishops for both sides attack?" etc.
I know this is over 10 years old, but cool idea, I've never heard of this technique before.
And now it's possible to play live chess with "blindfold" pieces (removes the icons from the board). So now you can find opponents to play blindfold with at any time, even if your opponent can still see the pieces.
Of course it wont let you make illegal moves, and kohai said that a cursor icon will appear over a square where there is a piece, but not over and empty square. You could also look at the move list or the captured pieces to help.
But this would be a good way to practice. As you get better you could limit yourself from using those little aids.