I can't speak to how common in history but I know how messenger birds were (and still are trained). Messenger birds are not trained to fly to specific locations but rather to return home. Essentially, you raise a young pigeon's on a roof where they can see the city around them and slowly let them explore the surrounding area. Then you bring the birds with you when you travel and if you want to send a message home when you write a note on a birds leg and release it and eventually it will make it's make back to the roof where you raised it.

This still happens today but no longer for sending messages and instead for racing. If you search racing pigeon I'm sure you will be able to find a local group that raises, sell, and races pigeons.