This incredible idea is so easy and only requires tape, plexiglass, matt board, and hanging hardware. See the DIY post here.
The type of tape used in the post and photo above is plain brown craft tape. It looks great. For a different look, I think it would be fun to use Japanese tape. The choices are endless. Here are some options I saw on Etsy.
One other framing idea I saw over on Decor 8 is to apply the Japanese tape to a white frame. She used white IKEA frames which make another great and inexpensive alternative. See that DIY here.