After defeating the Canaanites, how did Joshua decide which tribe got a specific plot of land?
Joshua chapters 12-21 record the division of the land of Canaan among the tribes of Israel. As you said, this was done under the leadership of Joshua, but credit is given to God for the decisions. That is an interesting statement for most people, and it is a good question.
If you will look at chapter 14, verse 2, there is a hint given to help you understand the "how". "By lot was their inheritance, as the Lord commanded by the hand of Moses, for the nine tribes, and for the half tribe."
The key is that phrase, "by lot." The Hebrews used stones named the Urim and the Thummim that were kept in the breastplate of the high priest. These were used to make decisions, with the belief that God guided the outcome. If you will refer to the link below you will get a more detailed description of what they were and how they were used.
"Casting lots" was a very common way of making decisions for the Jewish people, and since Joshua 14:2 reveals that the division was done "by lot" then there is little doubt that this is how it was accomplished.
Hope this helps.