First I laid out the caps the way I wanted them. I decided to use skinny popsicle sticks to make a frame I could glue them to, so I positioned the sticks on top of the caps and used a glue gun to hold them together. (wood glue would be better, but harder to undo if you make a mistake, which I did a couple times). The frame ended up being double-thick, so I could glue the crossing pieces to the bottom of the top layer, then fill in the gaps so it all was the same thickness. (Hope that makes sense; pictures may explain it better:)
Then I began to glue the caps to the wood. I made sure to place them in each other's grooves to get them as tight as possible. The main part was easy, but the handle gave me some trouble and I squished some of the caps to make them slightly narrower until everything fit.
I hung it up in the kitchen! Like I said, it's a little fragile, but sturdy enough to hang on the wall just fine. I reinforced the corner caps with some extra glue when it was all done. Here it is!