A Cube is a custom draft set, typically designed to showcase the "best" cards ever printed in Magic, but sometimes with other thematic restrictions.
Discuss all things Cube here!
Even shuffling up random draft chaff can be a fun start. Any old cards regardless of rarity and color balance.
That was how Magic was meant to be played (page 5).
Then if you want a more curated experience you can design cubes carefully as if you were designing your own pet set. Or you can make "set cubes" that emulate a particular set. We have a Shadows over Innistrad cube for example.
Check out cube cobra.com for several example cubes. Also there's several good podcasts out there like lucky paper radio, solely singleton, and "the 540".
Honestly, if you have a bunch of draft chaf from a set you really liked, just shuffle that up and start drafting it. You'll figure out what you and your playgroup like and don't like, and you can start picking up cards that pick those play styles from there.
The nice part about cube is you really control the play environment. Power level, synergy's, fan favorite cards, etc.