Select the songs for your mashup. You do not necessarily have to like the entire song. If you only like part of the song, use just the part. The technique is known as sampling. The most important part of choosing music for your mashup is to pick songs with similar beat patterns and in the same key. They will sound the best when listened to simultaneously. Download the music tracks to your computer's music library by either copying them from a CD you own or purchasing the rights to them through online services such as iTunes or Rhapsody.
Download a software that will allow you to important your music tracks and edit your mashup. There are several softwares available online for free legally thanks to open source software. Others can be purchased. Some examples include Audacity, Garage Band or MEF.
Import your tracks into your music editing software. Read your software's manual to determine how to do this, but most software programs only require that you click "File" then "Import Audio." Your tracks will appear as a line in the software which moves up and down to visually resemble the length and pitch of the track.
Edit the tracks within the software to create your desired mashup song experience. Moving the tracks on top of one another will allow them to play simultaneously, while using the "Cut" function will allow you to trim the clips to create smaller samples for your mashup.
Save your mashup as a new MP3 file with a unique name to your computer's hard drive so it can be shared and replayed later as one electronic music file. Do this by selecting "File" then "Save As".