You've gotten some excellent advice and information so far, but do you know how to tell when a hen is going broody? That's key to being able to gather very fresh fertilized eggs for her to sit on.
When a hen of mine begins to go broody, she begins making what I call the "broody cluck". It's a very soft, rapid popping sound, almost inaudible. You may begin to notice very small feathers being left behind in the nest where she lays her egg. If you look on her breast, you'll probably see it's gone rather bald along the keel bone.
This is when I begin to salt away fertilized eggs from the hens I wish to have chicks from. Your broody isn't selective about whose eggs she will sit on. You can refrigerate the eggs or just keep them in a cool dark place.
The broody will lay her final egg and begin to sit on the nest. You will know she's serious about it when you remove her from the nest and she races right back on it. Then you place the eggs under her. It's best to mark the eggs with a lead pencil so you can tell which ones are incubating. Other hens love to lay their eggs in the nest with the broody in it, and soon you'd have a nest overflowing with eggs.
Unless you find a place for the broody to incubate her eggs without interference, some of her eggs may get broken when other hens climb into her nest. Broodies do their best work when they're in a place away from the commotion of the flock. When the chicks hatch, the babies will be much safer, as well.