Start out by applying glue to the "fingers" on the boards that will fit together. The glue goes down in the "U" shape but not on the top of the pegs - those don't get glue.
Then just fit one side together and tap it into place lightly with a hammer. Then glue and do the same with the other side. It should look like the picture below.
You can hit it a few more times for good measure if you really want to. Now you are ready for some nails.
Start the nails by putting one in the middle "finger" on each side of the piece facing up.
Then flip it on it's side and put one in the bottom of the side piece. After that flip it back on the other side and put one in the bottom there.
Now you are ready to glue and tap in the fourth board. Do the same thing with the nails: One in the middle on each side and then flip it each way to put in the two nails at the bottom of those sides.Now it's glued up and nailed together. It should be sturdy enough for you to handle without worrying that it'll fall apart and it's time to drive the rest of the nails in.
I numbered the nails here to show how I do this part - kind of like tightening lug nuts when putting a wheel back on a car, I try to nail them in alternating order. After the last "2" is in I put the 3s and 5s on that side then rotate it and put in the 4s and 6s on that side, turn again, 3s and 5s, etc.
The last thing to do is to nail in the strip that the frames will sit on. I guess this is a separate strip so that you can replace it when it wears out after years of removing and replacing the frames. I can't actually imagine this happening with my hives so I glued mine in. I may be screwing the next generation of beekeepers to use my boxes provided I did everything else right.
One thing I recommend is that you go kind of slow, making sure your nails are headed in the right direction. If you go too fast your nails will either bend or angle out of the wood which although not disastrous can be annoying.
