Byron,
Depends on the particular airplane you have, and how the system has been modified.
The original Cub Special (PA-11) came with a single fuel tank in the left wing-18 gallons. This was also true of the first PA-18's. The right tank was an option.
As such, the left tank has a front and back fuel pickup port, so that if you are climbing or descending, fuel will continue to flow.
Since the right tank was optional, it only had a rear fuel pickup port, for simplicity, and to keep down extra expenses.
As a consequence, in a steep descent, for example, you could unport the fuel pickup on the right tank if you were in a descent long enough to run the fuel out of the header tank. All these airplanes were originally placarded to use the right tank only for straight and level flight, or words to that effect.
So, the "normal" procedure would be to takeoff, land, climb and descend on the left tank, and cruise on the right tank.
I always admonish students not to run the left tank dry enroute for this reason.
Now, many Cubs have been modified in many ways, including having the header tanks removed, and some have even had a second fuel pickup added to the right tank, I believe.
As always, you need to know specifically how your airplane is equipped.
There's a long thread on here on this subject.
MTV