I agree with Jay (hi Jay!!), this should be fairly straightforward to do and like Mark says you might need a DAW which will help you load the Vocoder software and route your ins and outs.
Remember that for the vocoder to work you need two signals, a modulator (your voice) and a carrier (synth sound). You need to set the vocoder to receive your computer's microphone as the input and then the vocoder's out to your speakers or headphones. Plus your keyboard connected via MIDI, which will be how you control the plug-in's built in synthesizer.
If you want the straight synthesized sound you can use your laptop's mic and get a decent result, if you want to hear some unprocessed voice a better mic will be in order and you will need to be careful with feedback (that's why Jacob Collier is using headphones).
Depending on the DAW and plug-in you use there will be a blend/mix knob and everything will happen under the hood or you will have to set a separate track and more involved routing to get it working.
I know Audacity (free) has a Vocoder function but I don't think it works live. Logic Pro has one and NI's Reaktor has many ensembles that do this. Back in the day my favorite was NI's Vokator, sadly discontinued years ago.
One of my favorite uses of a Vocoder is Imogen Heap's Hide and Seek: