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 want something simple to get started you could build this class A amplifier: 

![enter image description here](https://i.stack.imgur.com/xO68Y.gif) 

(from [this excellent site](http://www.electronics-tutorials.ws/amplifier/amp_5.html)). 
\$R\_E\$ stabilizes the DC setting, the bypass capacitor \$C\_E\$ is needed to allow an AC signal to change the output, otherwise \$R\_E\$ would try to keep the output constant.  

A class A amplifier is not very efficient. There will always flow a current through it to keep the output at Vcc/2.
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.