We used repurposed materials and things we had lying around the shop to build our frame. Since your project will likely be different, I'll just go over general details here. There are lots of great frame-building tutorials online, so take a look around to figure out exactly what will work for you.
We used an old, broken shoji screen we found in the basement. The paper is torn in places, but the wood and frames are still in great shape, and it has a really interesting look to it with the additional wood trim inside. Perfect!
You could also repurpose an old picture frame, find an old mirror or painting at a junk shop, or buy something new that suits your vision.
We unscrewed the hinges holding the panels together, then cut the screen down with a chop saw and moved the bottom of the black frame up, to get it to the size we wanted.
The shoji screens were painted a shiny, glossy black. While this looks great on a screen, the gloss really reflected the LED lights in a way we weren't too crazy about. We wanted the lights to highlight the moss, not the frame. So we repainted the front of the frames with the blackest black we could find -- BLK3.0. This paint is really really black! It completely killed the NeoPixel reflections.
This paint has a fascinating backstory. Here's a delightful episode of the 99% Invisible podcast about VANTA black and BLK3.0 and Anush Kapoor -- settle in for a good listen while you're waiting for your paint to dry.
After some experimentation, we decided the lights looked best when they were set above the frame by an inch or so. This way the lights would illuminate the tips of the moss instead of getting lost in the depths. We built a secondary frame from 2" corner moulding and stained it to match our existing wainscot. We used corner clamps to glue the corners together, and reinforced them inside as well, making sure to leave a channel for the LEDs.