Lamps aren't particularly expensive, but if you want to make your own little portable lamp, Instructables user Saiyam has a guide to make one with a rechargeable power source.
The build here isn't too complicated, but you'll need to know a little about electronics to get the job done. The end result is an super-bright little lamp that you can move around to wherever you need it without worrying about a power cord. Head over to Instructables for the full guide.
Make Your Own Desktop LED Lamp [Instructables]