I don't know if this is in the same field as what you're talking about but I'll give it a shot:
For knights whenever they move, I try to picture an octopus of where ever the opposite color square it is going to land on. Usually up till the 2nd-3rd depth (2nd or 3rd knight move) to see whether the knight has real annoying prospects or it's just a simple development move.
For bishops/queens/diagonals I like to look at the entire diagonal they are on (even with obstructions and own pieces in the way) to see future diagonal plans or tactics. It's always good to visualize how your pieces support, attack at a diagonal and make moves accordingly.
For rooks/queens/files I usually keep my rooks on the semi-open/open files which is typically where you put them in order to attain file control. Now if the file is semi-open, I like to see if I can exploit and pins which usually wins a pawn or a minor piece - atleast at my level.
If you are just trying to learn the actual square names, I'd suggest reading a chess book. You would just get used to all the e4 lingo because it's all practise. Once you start talking the language of chess, it will be alot easier to bridge the gap between an average and decent chess player.
In IM Rensch's Full Board Awareness video (http://www.chess.com/video/player/achieving-full-board-awareness) he says that it is a good idea to learn many things for visualisation.
For learning square colours, the technique I have developed is to give the letters "odd" and "even" corresponding to their position in the alphabet. A, C, E and G are odd and B, D, F and H are even. When their is an "odd" letter and an odd number, the square will be dark and vice versa (eg. d4, a1 etc.) however when it's an "odd" letter and an even number and vice versa, it will be a light square (eg. d3, a2 etc.)
Saying the "brother" square intantntly I'm working. It doesn't seem like there is a particular technique except just practice.
The other one's such as naming the squares on a diagonal or getting the knight to a square on the other side of the board I don't have a technique for and it seems like they'll be hard. I would like to know: Does anyone have any techniques for these excercises?
Thanks.