How do I play this game?

Left-click on a piece and drag it to the desired location. Release the mouse button to drop the element there.
Press "E" to toggle on/off visibility of non-edge pieces
Press "Q" to show/hide preview tile
Space bar to show/hide non-composite pieces (pieces made up of two or more atomic pieces)

Can I create my own puzzle

Yes. First you have to register to and log in.
After that go to "My Profile" and click on the "Create puzzle" button at the bottom of the page.

Can I share a puzzle with other people

Yes. First you have to generate a puzzle by selecting the desire cut type and number of pieces.
After you created the puzzzle just copy the url from the "Share puzzle" field at the bottom of the page