Create new document, fill it with background color of your desire (I chose greyish blue), and apply the following filters:
- Noise (Filters menu - Noise - Add noise)
- Sponge (Filters menu - Artistic - Sponge)
- Textutizer (Filters - Texture - Texturizer)

Important! After applying each effect, immediately hit Ctrl-Shift-F (Fade) and fade each filter down to 10-20%.

I overlayed my scanned image for reference...

Set foreground color to orange, switch to Pen tool (P) and create a shape of puzzle piece, using pencil sketch as reference.

Here is the completed shape - I decided it does not need to be very symmetric!

Open Layer menu - Layer Style - Blending Options (or simply double-click on layer) and apply the following layer effects:

- Outer glow: black, size 3px, mode=overlay
- Bevel and emboss: size 2px, highlight mode=overlay, shadow mode=overlay
- Pattern overlay: choose any pattern that fits :-) blend mode=overlay, opacity=10-15%

Duplicate this layer, change orange color to much darker (brown), then move this new layer down (so that it is behind original orange layer) and then move shape a little up and right. This will give additional depth to the puzzle piece.