The following 5 programs are great tools to work with audio on your computer. All of these are completely free, open-source software that can be used for personal and commercial use.
Audacity is an audio recording tool. Not only can it record audio from multiple sources, but it is used for post-processing for any type of audio. Audactity is a great option for podcasts. You can add effects such as normalization, trimming, and fading in and out. You can take the lyrics track of off songs to create karaoke versions, you change the pitch or speed of an audio track, and is great for capturing audio. Audacity is available for Windows, Linux, MacOS/OS X, and Unix.
Link to download Audacity
This program is a great tool for creating music. You can import audio your created yourself, or create synthesized music in the program. You can import a midi keyboard or use the keyboard in the program. You can listen and edit each track individually to perfect your music. It can write and read customized presets and themes. Audio can be exported in the OGG and WAV file formats, and the projects are saved in the plain XML MMP or compressed MMPZ file format. LMMS is available for Windows, Linus and Mac.
Link to download LMMS
Ardour is a great tool for piecing together recorded tracks. Its a hard disk recorder and digital audio workstation. You can play around with different effects, similar to audacity, but its designed to work with multiple tracks. This program is available for Free BSD, Linux, Windows and MacOS.
Link to download Ardour
Mixxx is a DJ mixing tool. Its a great program for live broadcasting, dances, parties etc. You can save and record music you create and set it up to auto DJ. It can be controlled with MIDI and HID controllers as well as time-code vinyl records. Its available for Windows, MacOS, and Ubuntu.
Link to download Mixxx
Spek is a spectogram analyzer for mp3 and other audio files. It visually represents the quality of an audio file. Its a great tool to use for a quick way to visually see the quality of your audio file.
Link to download Spec