Step 1: Find the parts!
The input and output capacitors depict the frequency response of the circuit e.g. The lower the input capacitor, the more bass is cut. This is good if your looking for a nice Trebly overdrive. Otherwise, this capacitor can be increased to any value. The values of these components doesn't particularly matter if your just looking for a simple distortion circuit.
The 100Ohm Resistor that is just above the Diodes can be removed to make the output wave much 'Harsher'.
The 100K resistor at the base of the Transistor mainly depicts the gain. Increasing this resistor increases the gain up to a certain point (It changed the bias of the transistor).
Edit: I have now included my new circuit diagram for the much more RAW! Distortion. Go to the last page for sound samples! Unfortunately, with this new circuit, the distortion isnt so epic at 1.5v :(
For this new circuit, i used a BC337-25, a much more gainier transistor.