Now, there are two different ways that people usually care for a broody. Some people will leave her wherever she decides to make her nest. I have tried this, and it never worked for me. If she makes her nest outside the coop, this is not even a viable option, since she could be exposed to the elements and predators. If she makes her nest in a nesting box like mine did, other hens will try to lay eggs there as well. You can try marking the eggs that your hen is incubating and removing the ones that the other hens lay, but pencil marks wear off easily and I don't really like the idea of putting marker ink on my eggs since they are porous. There is also the chance that the eggs that the other hens lay in the nesting box with the broody hen could start developing an embryo if you leave them there too long. Unfortunately, what could also happen is that when the other hens force the broody hen off her nest to lay their eggs, she may get confused and go sit on a different nest!
Really, your best option is to separate her from the others. A good way to do this is by making a cozy nest for her inside a dog kennel placed inside the coop. If you don't have a spare dog kennel or can't find one to buy, you can make something similar by framing out a cage with 2x4 boards and chicken wire, or welded wire fencing. If you do this, keep in mind that day old chicks are small enough to squeeze through both of those types of fencing, and you will need to add hardware cloth (a wire mesh with very small holes) to at least the bottom half of the cage. Be sure to add a door!
I call this cage for broody hens the broody box. Inside you will need to put a pile of straw, wood shavings, or your preferred bedding for her nest, a small feeder and waterer. You may or may not want to put some of the bedding inside a bottom of a cardboard box, so that the eggs do not roll out of the nest. Just be sure that if you do that, you make the edge very short, so that the newly hatched chicks can get back to mama if they should wander out of the nest.
New baby chicks, during the first few hours of life, are very uncoordinated, weak, and chill easily. They should remain under mama until they are fluffy, fully alert, cheeping, and walking around. Don't leave any corners in your box, where a clumsy chick could get stuck away from mama, if this happens he could chill and die.
Here is a box I set up for my Black Langshan hen:
Once you have your broody box set up, wait for night. This is very important. The reason why some people choose not to move their broody is because if you disturb her too much, you could cause her to leave the nest permanently. By waiting for night, you can move the broody hen at a time when she is sleepy, and less aware of what you are doing. Chances are, if she is a good broody, and you quietly move her during the night, causing as little disturbance as possible, she won't even realize that she was moved.
When you take her off her nest, be very careful that neither of you bump the eggs. If she is too alarmed when you take her off, she could smash the eggs. Put one hand under her body, letting her legs hang down between your fingers, and use the other hand to hold her wings down to her body. Then hug her snugly against your body. If you do this properly she should struggle very little, if at all, especially if she is accustomed to being held. Put the hen in the nest first, then tuck her eggs under her. If you put the eggs in the nest first, there is a greater chance of them being smashed.
If all goes well, all you have to do now is keep her food and water filled up, and wait 21 days! Often, eggs hatched by a broody will hatch a day early, so I would mark 20 days from the time she started sitting on your calendar. Here are some cute chicks to keep you going until you have your own!