This is a beginner technique, so don't hate on me if this seems basic.
This Instructable also doubles as a hands-on basic introduction to the wonders of Adobe Illustrator for novices. Making this model took me about 10 minutes. I am going through EVERY step in extreme detail for novices, but don't be scared off by the length of the tutorial!
You will learn: a technique for making such necklaces (or laser-cut cut outs from other line art), a mechanism for uploading your design to a fabrication site and recommendations for how to get it fabricated effectively and cheaply.
You will need: access to Adobe Illustrator CS2+, the internet, a bit of money (not too much) to pay for the fabrication. Illustrator is not cheap, but perhaps you know someone who has it running on her/his computer? At your school somewhere? It's a common design program, so you'll find it around somewhere.
A couple of notes:
My screen shots will be using AI CS4. They should be generally applicable for CS2 and beyond. Illustrator is TRICKY, so don't get discouraged if you find yourself stuck. This procedure should avoid some of the most common pitfalls. If you hit a wall, Google is your friend, as is the Help menu and Adobe online help. Search, and use it liberally.
I am NOT affiliated with any fabrication site. I have used Shapeways for 3d printing and Ponoko for laser cutting and found pros and cons for each. Generally, I think that online fabrication is awesome, and everybody should try it!
The speech bubble design in the photo is something simple that I made, a similar version of which could easily be created using this technique. I wanted to share a photo of something physical, although in full disclosure, that was 3d printed rather than laser cut. 3d print design is for another instructable another day...