The actual troubleshooting maxim is quite simple: Follow the frame from source to destination. Each station should be forwarding the frame to a correct destination; router to router; until the final destination is reached. If someone doesn't forward the frame correctly, and if the destination address is valid, then that station is misconfigured.
To know what the expected forwarding will be from router to router it is necessary to understand the underlying subnet masking being used by the routers and by the nodes. The meaning of the dotted-decimal IP address can only be ascertained by applying the mask using binary arithmetic to determine which bits are used to represent the network, the subnet (or subnets), and the host.
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