Dynamic routing protocols automate tasks:
Neighbor Discovery. Routers find each other by exchanging hello messages. You don't configure neighbors manually.
Route Advertisement. Routers share what networks they can reach. This builds a picture of the entire topology.
Path Calculation. Each router independently calculates the best path to every destination using the shared information.
When topology changes, routers detect it through missed hellos or explicit notifications. They then recalculate paths. This process is called convergence.