This piece is made from folded paper (constructed of 2 origami techniques called Golden Venture and Lucky Stars, I believe). There are numerous how-to create 3D origami videos on YouTube (vases, boxes, animal shapes and more), but they're usually rather long or more complex than I like to include here. But if you're interested, here's a link to a video showing how to construct the basic pieces (the triangles). And here's a link on how to make the lucky stars.
Other paper art
Even cutting away bits of paper can create a beautiful result (think of a paper snowflake taken to the next level).
The video below is a stunning example of paper cutting. The result is beautiful (Note: after the first few seconds to see the technique, fast forward to the end to see the results).
There's also quilling. The image below is a good example, but also here's a link to the artist's Flickr page (she has some gorgeous creations).
There are so many beautiful designs that can be made with something as simple as paper. I'm in awe (and I wish I had the talent and patience to create things like this).
Have a wonderful day!