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.
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: