A host wants to send an IP datagram. The host checks its routing table.
If the datagram cannot be delivered on the local network, the host extracts from the routing table the IP address of the router associated with the destination address. The router's IP address is then resolved to a physical address using ARP.
The datagram (addressed to the remote host) is passed to the Network Access layer along with the physical address of the router that will receive the datagram.
The network adapter of the router receives the frame because the destination physical address of the frame matches the router's physical address.