Powering a Multi-Stage Lift

My team is doing a one stage lift with a smaller internal stage which lifts our cube intake similar to the Ri3D team: Greenhorns. But we have no idea how to power the first stage and can’t tell from the video. We were going to do a chain driven lift but don’t know how to actual get the chain to lift the stage.
It would be a great help if you can try and explain in detail because it is my first time taking a heavy lead on design. Thanks!

Greybots 973 has a series on Lifts for FRC that I found really great. Here’s a link to part 1: https://www.youtube.com/watch?v=wZ6a6dc4BGg.

This is actually the video that inspired The GreenHorns’ elevator design. It does an incredible job of explaining how the mechanism works!