Import the first track that you would like to mash up into your music program and delete the portion of the track that comes before the lyrics and before the first drum beat.
Play the song and and listen carefully, placing markers at the beginning and end of the fourth or eighth bar of the song. In some programs, you can place a marker by hitting the tab key until you reach the section that you want to mark, and then pressing "i" on your keyboard. Set the song's tempo to the marked region of the song, which will be either four or eight bars. To find the tempo setting, click on the tab marked "properties" then select "edit tempo" from the from the drop-down menu.
Add two new tracks to your program and leave them blank. Create a fourth track and import your second mash-up song into the track. Edit the pitch of one of the songs in track one or track four by clicking "properties" and "edit pitch" from the drop-down menu of your program. The pitches and tempos for the songs should both match.
If you decide to include vocals, delete and insert the vocal tracks where you want them to be. Place markers at the beginning and end of target vocals to stay organized. You can add and delete the portions of the vocal tracks by cutting, copying and pasting them.
Listen to your mash-up and alter it as you desire.