Download a free or open-source recording program. Many free programs exist with advanced recording and mixing capabilities, including Ardour, Audacity, Linux Multimedia Studio, QTractor and Rosegarden. Read the specifications of each program that interests you, and choose a program that supports multi-tracking. Check the system requirements, and verify that it will work with your operating system.
Locate the songs that you want to mix together. If the songs are on a CD, you need to rip them to your computer using a CD copying program, such as iTunes, WinAmp or Windows Media Player.
Import the songs into your new recording program. Open the program, create a new project. Click "File" and "New." Select the "Import" option. Import each song file individually, and they should appear stacked on top of one another in separate horizontal recording spaces.
Arrange each song file on the timeline. Your time line looks like a horizontal ruler, appearing across the top of your project window. If you want certain parts of each song to align, drag them to a matching spot on the time line, while keeping each file on its respective track, the horizontal recording space or layer.
Delete unwanted parts of any song file by using the "Scissor" button to split up the file into segments and delete the unwanted parts. Some programs offer a "Cut" or "Split" option, which serves the same purpose.
Balance your levels. In the right column of each track, there is a "Level" or "Volume" indicator, sometimes appearing as a knob and sometimes as a slider. Adjust the volume indicators to balance the volume of each song, bringing them into harmony. If a particular song plays too fast or slow, select the track with your mouse and locate your "Effects" menu. Select the "Speed" option to speed up or slow down the file until it matches the other. Not all programs offer this feature, so choose song files with similar tempos for best results.