You can take an existing light, or use one of the many nifty Instructables. I used the same concept to make a flower LED light for my daughter (http://www.instructables.com/id/LED-Flower-Light/)
You will need:
A piece of pose-able wire (like a bit of coat hanger. You want the wire to be easy to bend and hold its position. After you bend the wire back and forth over and over and over, it will eventually break; if you pick something too soft it will break quickly.)
Heat Shrink Tubing (for electrical work, available at hardware stores, auto parts stores, that internet thing)
The light you want to make pose-able
Slide the wire of your light, and your pose-able wire through the heat shrink tubing. If you are assembling a light, you may want to slide the tubing on as part of the assembly (such as before you attach the wire to the USB end.)
Use a heat source (responsibly) to shrink the tubing.
The tubing will hold the pose-able wire and the light together, so you can point your light where you need it.
The tubing is available in bright colors, so you can have something more decorative than just black.
If you put the tubing on as part of building or modifying a light: heat shrinks the tubing. Duh, right. Just plan ahead: if you are going to do some soldering, make sure you slide the tubing out of the way, and mind where you swing you soldering gun; you do not want to shrink the tubing early.