First, find a song that you feel comfortable singing in your natural register.  Record yourself singing it three separate times, and layer those together using your choice of audio editing software (I chose Audacity for mine, since it’s free).  Do not use any effects for this, so try to pick an acoustic song relying mainly on the vocals.
Sing the whole song straight through each time, and make sure to trim off and align them correctly so that they start at the same time; You’ll have to zoom in considerably.  The point of singing through completely is to eliminate the possibility of just singing the chorus or another repeated verse and editing them together; it will not sound like a trio that way.  You may be alarmed by how different your singing voice sounds on a recording compared to what you believe it to be, but don’t worry about it too much, just get used to it–that’s how it sounds to everyone else when you sing.  

Set one recording as Stereo Left, one as Stereo Right, and one as Mono for best results.

Tips: 
Listen to the song on your headphones while recording so that you stay on track. 
Warm up your vocal cords, otherwise your voice will crack.
Try to keep the mic away from your mouh and nose–the sounds of your breathing may detract from your results.  

Once finished, upload to SoundCloud.