Distance vector routing works by routers sharing their known distances to all destinations with their neighbors. Each router starts knowing only the distance to its immediate neighbors. When a router receives distance vectors from neighbors, it checks if it can reach any destination with fewer hops by going through that neighbor. If yes, it updates its routing table with the shorter path. This process repeats periodically or when changes occur, until all routers have the shortest paths and no updates happen anymore, called convergence. For example, Router A initially thinks C is 4 hops away, but after hearing from Router B that B can reach C in 2 hops, and since A is 1 hop from B, A updates its distance to C to 3 hops. This exchange continues until no router can improve its routes. RIP uses hop count as the distance metric and limits max hops to 15 to avoid routing loops.