Getting the Horadric Cube
You will acquire the Horadric Cube as part of your questing through Act II. It's located in the Halls of the Dead, guarded by Bloodwitch the Wild. Defeat Bloodwitch and take the Cube. Since it's available on Normal mode, you will get the Cube early.
Horadric Cube Basics
The Horadric Cube can either be carried in your personal inventory or in your stash (most people keep it in the stash). It takes up a 2x2 space but has 12 slots inside. For this reason, some players short on stash space will use the Horadric Cube as temporary storage, tossing items onto the ground while they do their Transmutes. Just don't forget to pick them back up.
To use the Horadric Cube, place the correct group of materials inside the Cube and click the Transmute button at the bottom. If you don't have the right items, it simply won't do anything.
Transmutes are not reversible. Make sure you know what you're making before you combine!