The last step of actual construction is the back doors. I designed the cabinet with both the top and bottom halves of the back as large doors, so that I could easily access all of it. In between was just a thin brace of about two inches, for strength.
The doors are just rectangles cut to size, and by "size" I mean about a half inch smaller than the space they go into, to allow room for the hinges and such. This is going to be in the back so you don't have to make it pretty, but don't neglect sanding the edges. You'll want to jigsaw out finger-pull notches, plus at the bottom, a notch for the power cable to come out of the case.
Then heft the door into place and screw in the hinges, being sure that you do so in such a way as to allow full freedom of movement. This is a two-person job, but I did it alone by using a bunch of shims and temporarily clamping pieces of wood into place to hold the doors up long enough to mark the points the hinges should affix, then affixing them. I was worried I'd end up off alignment too much this way, but it worked out fine.
Putting in the latches was a lot more difficult. If there's a trick to figuring out where to put them so that they line up perfectly on the inside of a cabinet when you can't be on the inside when it's closed, I don't know it. For me it was a lot of trial and error.
In the end, though, it wouldn't stay closed even when they were lined up right. The hinges had to be "wracked" -- closing them on a screwdriver to 'stretch' them a bit -- and then more tweaks, which I really didn't get to see, were done on the positioning, and in the end the latches still only barely hold.
Again, though, the doors will be in the back against the wall, so it doesn't have to be quite perfect. Just enough to discourage mice from moving in, really.