Distortion and reverb mostly. Something that you can control the harmonics with would work nice such as Cristortion. But a clipper would do it like GClip. EQ down the low mids a little after the distortion.

I don't have GCclip, I do have distortion. I guess for the clip effect I could boost the output on the effects and then turn down the main volume off the vocal on it's track volume. The distortion sounds kinda meh.

GClip is free, and located here:
http://www.gvst.co.uk/gclip.htm

Thank you so much. I'm using Adobe Audition 3.0, do know know how I can get this into the program and open it up?

If Audition supports "VST Plugins" (I don't use it), put the GClip.dll file into either "C:Program FilesSteinbergVstplugins" or "C:Program FilesVstplugins" (or technically any folder you want) then in Audition, find a setting that lets you specify a VST folder - point it to your Vstplugins directory

^ Audition does support VSTs, so you'll be fine.