I used to get birds in my fireplace ALL the time. They would perch on the top of the chimney and fall in, I guess. I put wire around the chimney, and problem solved.

This is what I would do to get them out: if they are flying adult birds, I would put the dogs out, of course. Then I would close the drapes or blinds and turn all the light off in the house. I would open the front door, so that the house was dark, and only the open doorway was lighted. When I opened the door the bird would almost always just fly out the door. One or two got confused and ended up in the house somewhere, I just threw a towel over it and put it outside. A baby bird should be even easier, if it's not flying really well.