Lilypad Arduino is the only sewable microcontroller in the 20 $ range. You need a programmer to burn your sketches on the tiny Atmega 328 on board. You can use a standalone FTDI breackout boiard or another Arduino. Check this tutorial for more info about it.
There are many resources online about how to use lilypad, besides wonderful Leah Buechley’s lilypad home, you have to give a look at Open Softwear (from 1scale1). It is a free book (CC-NC-SA-2.5) introducing basic concepts about microcontroller programming.
The 104 pages long document was made by T. Olsson, D. Gaetano, J. Odhner and S. Wiklund. It contains tones of illustrations, an introduction to programming, help in the use of conductive materials, and explanations about basic electronic components. It is perfect for beginners and fashion-oriented technologists. It was designed for people using the inexpensive Arduino USB board, but from here it should be possible to jump into using other systems like Arduino Lilypad.