How does the router use IP, subnet mask and gateway information to establish a route to a host on another network?

So I understand how subnets are used to create domains so address spaces can be distributed efficiently. I understand how the subnet masks are used to declare which part of the ip represents the network id. What i don't understand specifically is this; a router uses the network id without a host id to reach another router. How does that router know to which host the incoming packet should be sent to? Somehow I have the feeling that I misunderstand something fundamental.

If the question is too complex to explain in comments, perhaps someone could show me the way to an easy-to-understand reference on this. If this post doesn't comply with sub rules, please forgive me.

Tl;dr : how does the destination router know which host a packet should be sent to?