It really isn't that complicated.

With no cable tension, derailleur goes to the most relaxed position. For the rear, it's the hardest gear.
Adding cable tension allows you to go up the cassette. The cable is "pulling" the derailleur up.

What does this mean? When there's not enough cable tension, the derailleur refuses to move up. So you need to increase tension.

How do you increase tension? Well, for small adjustment, use the barrel adjuster. For large adjustment, loosen the nut and tighten the cable.