The Machine Frame
Putting the frame together can be a little bit of a puzzle. I think I "got it" on my third try, since I didn't have to take anything apart to put it together that time. Click on any of the following images to enlarge it.
Bridge Axis Installation
The bearing shafts have the most "give" since they sit in deep sockets on each side, so we start with those, going from side board to side board.

Lay down one of the side boards, place the shafts into their supports. Gently slide on the axis stage, holding it till it rests in place on the shaft supports. Then get the other sideboard in position with one hand, and rock the other sideboard up with the other to line up the shafts with the shaft supports on the other sideboard. You can pin at least the top shaft in place with a thumb while you do this. Then seat the shafts into the second side board.
Back Board Installation

Next we install the back board. This goes before the board that goes on the bridge. Really.
Carefully spread the sideboards apart while keeping the bearing shafts in their supports until there's enough room to get the back board in place. It's not too hard to manage.
Bridge Backboard

With the bottom of the sideboards moved in close enough to hold the backboard in place, we then install the board that goes behind the bridge axis. Once it's in place, push the sideboards in to pin both backboards. The front of the sideboards should still be gapped a bit wider, though, so that we can install the front board later.
One thing about this board that confused me until John explained: there's a small hole in one side. That hole has no function with respect to CNC milling. It's for hanging up the board while painting it. So it doesn't matter which way the board goes.
Threaded Rods

In the meanwhile, we can insert the threaded rods to hold together the back side of the machine. Make the nuts snug enough to keep the back end from falling apart, but not at all tight since we still want a lot of play. Once they're at all tight, the pockets that the back boards are set into will grip them, so leave them pretty loose for now.
Table axis installation

Turn the partially assembled frame around to the front, and put the table axis shafts into the supports on the back board.
Table Axis Slide

Then the table axis slide goes onto the shafts.
Finally, the Front Board

Now we can put in the front board, removing the screws from the Delrin nuts, popping the board in place, then running the screws back in.
Snugging Up and Adjusting
Now that the parts are basically in place, go around the frame squaring and snugging things up a bit. Don't tighten the nuts on any of the shaft supports, yet. Move the frame around a bit, lift it off the table and set it down again at different angles. Let the parts settle in to their places. Wiggle things. Just use your fingers on the nuts, you may need a screwdriver on the screws on the front board, but don't tighten down a lot, just snug it up.
Once things seem pretty well seated, move the axis slides back and forth along their travel. Rotate the shaft supports to see their effect on the movement of the slides. You'll find that there are "good" positions for the shafts and their supports, where there is little or no resistance to movement anywhere along the travel of the slide. There may be some residual friction at some points of the travel, but it should be very minor.
If it appears that you can't get the friction down low enough on one of the shafts, you might consider partially disassembling the machine to swap shaft supports or shafts from place to place to get things practically frictionless.
See John's notes on assembling the A4 for more guidance on this, he's detailed it very well.