If the new tumbler is a true replacement, the segments--little brass cylinders of different lengths---can be swapped from your old lock to the new. It's the configuration of these that determine the shape of the key that will cause them to line up and allow the lock to rotate.

It's kinda tedious, but fun nonetheless. These segments look like pieces of cigarette lighter flint. Don't get them mixed up.

You'll figure it out. It's like solving a puzzle.