Final answer:
The rats in 'Mrs. Frisby and the Rats of NIMH' found out about the doctor looking for them through their established network of communication, lookout system, and ability to read human language.
Step-by-step explanation:
The rats in the book 'Mrs. Frisby and the Rats of NIMH' found out about the doctor looking for them through a sophisticated network of communication that they had established. They had a lookout system in place where they would keep an eye on what was happening in the human world and share information with the other rats. They also used their ability to read and understand human language to gather information from newspapers and books. This allowed them to learn about the doctor's search and take necessary precautions.