Router A only knows the networks that are directly connected to itself. For instance router A only knows router B by the shared network AB. Router A knows nothing about network BC. In order for router A to know about router C or anything that it is not directly connected to, router A must have a route table. There are a couple ways to do this. For instance, you can set a gateway of last resort for router A to be the B-side of network AB, and vice versa on router C. It is important to understand that in order to route to/from any networks, both sides must know how to get back. You could use static routes such as
on Router A:
IP route {network C} {netmask} {Network AB}
the first instance is the destination, the second is the subnet mask of the network(s) and the last is the path for the route to follow.
To make this work, you would also need to input the following on router C:
ip route {network A} {netmask} {nework CB}
this would allow you to route from network A to network C. This is a very basic static config, of course routing protocols can be used to advertise this dynamically, but Choosing routing protocols really depends on the situation and the size of the network(s) involved. This should at least allow you to push packets between endpoints.
