Routing Table
The Routing Table is the tool that you use to define a set of rules/conditions that other machines should check for. Right-click with the Routing Table in hand to open its GUI to type the instructions. The Routing Table has an built-in manual that explains everything you need to know. When you're done, place the Routing Table into routing machines, and they will check the conditions and perform an action if those conditions are true. The most common Routing condition that is checked is the Destination condition.
There's a way to copy a Routing Table so you don't have to type it out every time, but I haven't figured out how to do it yet.
Golden Railway Ticket
Right-click with the Golden Ticket in hand to set its Destination. Now you can insert the Golden Ticket into any Locomotive to set the Destination of the Locomotive. After that you can remove the Ticket to use again. The Destination is just a name, a string of letters that you then check for in the Routing Table.
Routing Detector
Like all Detectors, place this next to your track. Insert a Routing Table, and the Routing Detector will check any passing trains if they match the Routing conditions in the Routing Table, and will output a redstone signal if they are true (if they match).
Routing Switch Actuator Motor
Insert a Routing Table for a list of conditions to check for. Any passing train that matches the conditions will make this Switch Motor to activate and divert the train down the side track.
Routing Track Kit
Insert a Golden Railway Ticket into the Routing Track, and any passing Locomotives will automatically have their Destination changed to the same Destination that is on the Ticket.