I had a 95 and could have fitted a double din. Mine had a cd holder compartment at the top I was able to remove
Remove the gear stick surround, take out the 2 black screws behind cup holder at top of dash. Take off the gear knob, now you need to remove the rubber gator. There are two black screws at an angle under the gaiter. The base of the gear surround trim is held in by plastic tabs and should pull free, pull gently at the curve (this trim is easy to break so be carefull.) it should come free and you can remove the surround altogether.
Remove your head unit.
Then there should be 4 screws they should be brass coloured, holding in the cage for the radio, remove these and the whole centre part will pull toward you. Disconnect the cigarette lighter and you should be holding the cage free of the console. The cd holder on mine was held in by four screws Remove these and you end up with the separate halves of the cage. Depending on how your head unit was fitted it may still be held together by the metal tabs you bent on the head unit cage.
Edit:
Found a pic in the workshop manual.
You dont need to remove the rear console box
I didn't actually fit the double din as I mounted a knocklink and Lambda link in the space, but I'm guessing you could make some brackets to fit a double din if the ones supplied don't fit.
Hope that helps
Edit:2.
I have attached the 1995 workshop manual as a PDF. Its not complete but its the only one about.
1993-1996 Subaru WRX Workshop Manuals.pdf