Start by listening to the artist's song you'll be remixing. Pay attention to song structure, melody, tempo and dynamics. If there are certain instruments or melodic passages that catch your ear, make a note to include them in your remix. Think about how you could transform the song into something new but equally exciting for a listener. Jot down any ideas or techniques that pop into your head. Make sure you know the original tempo of the track; if this information is not included with the artist's files, use a metronome to figure it out.
Open your audio recording program. Start a new session and create 3 new mono tracks. Locate the file folder where the primary artist's source material is at. You want this material in stem format, meaning every instrument track is its own file. Now find the stem containing the vocal track; import or drag the file into one of the mono tracks of your session, then mute the track.
Add a drum machine or sequencer to the second mono track and construct a basic beat. Because DJ remixes typically infuse elements of dance music into an artist's track, the beat should have a "four-on-the-floor" style and last for four bars. Do this by placing the kick drum on note counts 1, 2, 3 and 4 of each bar; place the snare drum on note counts 2 and 4. Now place the hi-hat on the "and" of 1, 2, 3 and 4 to give the track an upbeat syncopated feel. You now have a basic club beat as the foundation of your remix.
Add a synthesizer to the second mono track of your session and set it to play your favorite bass patch. Un-mute the artist's vocal track. Now highlight only the first four bars of your session, and turn your audio recording program's loop playback function on; press play. Using your USB or midi keyboard controller, play the synthesizer-bass track until you've located the key of the artist's vocal track. Write a basic bass line that fits with the four bars of your drum track and record it. Copy the four bars of your drum track and bass track, then paste them in the session so that you have sixteen consecutive bars of music. You now have the foundation of a remix.
Edit your remix to taste by adding other instruments, percussion or importing other stems from the artist's source material. Make it longer or shorter by adding or subtracting bars. Experiment by changing the pitch of vocals or only using a certain vocal phrase throughout the remix. Add effects like delay and reverb to different tracks or to the entire mix. Continue building your remix until you're satisfied with the result.