It might sound silly, but just close your eyes and listen. Your brain is very good at localizing sounds. Turn to see if the sound direction moves or becomes more distinguishable. Tilting your head or moving a few steps in any direction can help in some environments.
You'll develop an ear for it the more you practice. You might not be able to actually find the bird once you've found the tree. They can be hard to spot from the ground.
> Your brain is very good at localizing sounds. ... You'll develop an ear for it the more you practice.
My grandfather would be able to do this almost instantly. We would be out on his ranch and hear them all the time; every once in awhile he would listen, turn and point in a direction to show me where the bird was that he spotted, and tell me what kind of woodpecker it was. I never saw the bird myself as much as he tried to point it out to me.
The man had hearing and vision super powers to me. He would spot edible plants in overgrown pasture and woods, spot a particular type of tree in the middle of a bunch of other trees and hear the location of wildlife stalking about the woods. And it was insane how much information he had about the natural world around us and the skill to utilize it.
You'll develop an ear for it the more you practice. You might not be able to actually find the bird once you've found the tree. They can be hard to spot from the ground.