My understanding of it is that your vocals go in, get split up by a multi-channel filter, each signal triggers the synth at a different range, and then the original is mixed back in at a low level under the synth's output.
Honestly, you're better off buying a decent AutoTune plugin for whatever DAW you're using, since that's probably what they use in the studios for the tracks you mentioned.
That being said, my microKORG
has a pretty solid vocoder on it, along with some excellent sounds. The only downside is the analog knobs which make for really imprecise timing when you're trying to make an electronic track... best to add all the time-based stuff in after.