Question: I would like to build a simple audio amplifier using transistors. I know there are IC designs specifically for the task. But i want to use transistors so i can learn how to use them for amplification.

How would I go about designing an audio amplifier from just discrete components.

Answer: 
If you just want to build a transistor amp, start with the TAB books, or with Forrest Mims experimenters books (usually available at Radio Shack).

Learning how to DESIGN one for a specific application, and do it right, is a different matter. That takes SERIOUS study.

For fun, Radio Shack's datasheet for the TI [SN76477](http://mkv.itm.miun.se/personal/per/diy/76477/276-1765.pdf) sound chip includes a very simple complementary symmetry transistor push-pull amplifier. They call out Radio Shack part numbers for the transistors, but you can substitute 2N3904 (NPN) and 2N3906 (PNP) with no other component changes.
There is an easy schematic for a class A audio amplifier with a darlington pair. A darlington pair is just two transistors that square the gain of the first transistor(if you are using identical transistors). So if the first transistor's gain was 20, then the gain of the darlington pair would be 400. [This website](http://sci-toys.com/scitoys/scitoys/computers/solderless/amplifier.html) uses a darlington pair in the form of one transistor: