How should the Shimano rear derailleur chain routing be properly set up on a bicycle?

To properly set up the Shimano rear derailleur chain routing on a bicycle, follow these steps:

1. Thread the chain through the rear derailleur's pulley wheels.
2. Ensure the chain is properly seated on the cassette and chainrings.
3. Adjust the tension of the derailleur by turning the barrel adjuster.
4. Test the shifting by pedaling and shifting through the gears.
5. Fine-tune the derailleur's position and tension as needed for smooth shifting.