The distortion effect was first created by guitar players overdriving their amps so that the waveform would become clipped. A similar effect can be done in a free and open-source program called Audacity.

Step 1: What You Will Need

You will need:

A computer capable of running Audacity (Linux, Windows, or Mac)

Audacity

A guitar recording (can be done in Audacity)

Step 2: Getting Sound

Open Audacity and record/import something. It is a good idea to save a backup copy as a .aup file.

Step 3: Leveller Effect (Part One)

Select the audio track by double-clicking it and then apply the leveller effect by clicking on Effect...Leveller.

Use these settings:
Degree of Leveling = Heaviest
Threshold Noise = -35 dB

Then repeat that effect by selecting the track and clicking on Effect... Repeat Leveller

Step 4: Leveller Effect (Part Two)

Select the recording by double-clicking it, then click on Effect...Leveller.
This time use the settings:

Degree of leveling = Heaviest
Threshold Noise = -50dB

Step 5: Compressor

The compressor effect will reduce the overall range from soft to loud. Double click the recording to select it. Then click on Effect...Compressor.
Use these settings:
Threshold = -9dB
Noise Floor = -40dB
Ratio = 5:5:1
Attack Time = 0.2 seconds
Decay Time = 1.0 seconds
Enable "Make up Gain for 0dB after compressing"

Step 6: Equalizer

To make the recording sound better apply the equalizer effect. Double-click the track to select it then click on Effect... Equalization. Use the acoustic preset.

Step 7: Finished

Playback the recording. It should have a distorted sound. Export it or mix it with another layer. Have fun!

I have attached an example in MP3 and OGG formats. The OGG format will play directly in Firefox.