There are two ways of drilling the holes. The first method is to drill a hole in both the top and bottom of the brick, and thread the string over the small divider in the middle of the second. This is the most accurate, since you centrally align the hole on both sides. However, the threading is more complex.
The second method is to drill all the way through the brick, including the three connectors on the underside. This is less accurate, and more difficult to drill, since you must hold the drill perfectly vertical to ensure the exit wound is centrally positioned.
To expedite the process I took the second approach. To make the threading easy I used a 4mm drill which is large enough to thread the string without problems, but so large that it decimates the internal lug holes.
Notice that the bricks are gripped slightly off-centre. This allows me to drill a hole in the centre brick without hitting the vice's support bar underneath.
Slowly drip glue into the brick, so that the string is fixed. I did this only on the two bricks at each end of the bracelet. And, as per the picture, don't close the loop!
I had tried threading elastic through the entire bracelet, but this caused it to hug the wrist too tightly. Being square plastic, this would leave marks if worn all day.
Step 6: Et Voila!
Note also that you can tighten and loosen the bracelet by fixing the bricks together on the back, as shown. Being LEGO, this can be adjusted time and time again, for different people. Especially handy for letting little sister borrow it!