Get the design:
There are a million sites online that can offer you motifs / murals / designs that can be used for a pendant like this one. I chose to use one I had with me. The motif is that of a beautiful bird depicted in the Indian mythology and probably is several cultures across the world.

Step 1: Gather the Stuff

Get the tools you need:
a. Brass sheet (2 inches X 2 inches)
I'm a big fan of metalsonline and here's the link to their brass sheets...
http://www.onlinemetals.com/merchant.cfm?id=1116&step=2&top_cat=79
I'm sure there are other sites better or as good...take your pick

b. A dremel or equivalent drill with a #60 and #67 or any large and small bits you may have handy
Since the audience here is across geographies, here's a chart of the drill bit sizes to inch and mm conversion that can help..
http://www.uboltit.com/drill-bits.html

c. Sand paper of various grits (mainly 400, 600 for coarse and 1000 or finer) and buffing wheels
I generally use the 3M pack for the finer grits and unbranded ones from the local hardware store for the coarse ones. The buffing wheel / attachment that comes along with the standard dremel pack is good enough for this.

d. Saw frame + blades +wax
5/0 or 4/0 blades should do the job for this project since there's not much in intricacy involved except the eyes of the bird where you may need a couple of 6/0 blades. I use Vallorbe simply because the local blades aren't as long lasting and sharp.

e. Cleaning solution and optionally the Reniassance polish
Any cleaning solution including regular soap water to take away the dirt, dust etc and I've heard some people being allergic to "non-noble" metals ;-) The Renaissance wax is works well to arrest the oxidation of the brass and is also supposed to take care of the allergy to brass coming in contact with the skin.
http://www.amazon.com/Renaissance-Micro-Crystalline-Wax-Polish-65/dp/B001DSZWEM

f. Lots of patience....goes without saying I guess

Step 2: Drill Holes and Start Cutting Away

To begin with, glue the design on the piece of brass that you have. I usually use a 1mm thick sheet that gives it enough strength to hold after its been cut. Any thickness that you are comfortable with works fine..stating the obvious: thinner the metal, the harder it is for it to hold the design.

I didn't take pics of me drilling holes on the design but I think you folks get the idea.

Insert the saw frame and start cutting away.

Step 3: Sand and Finish the Piece

Once done cutting all the unwanted areas and the accent lines, the real work starts!

As with any polishing, use several grits of sand paper to achieve the perfect gloss / matte finish you desire. I started of with the 400 and went on to 3000 and coating the finished piece with the renaissance wax. This ensures the oxidation of the brass is limited over time and is apparently skin friendly to folks who are allergic to certain metals.

All in all after several days of work, it turned out to be not too bad...