What I do is prepare the carrier/kennel first with nesting material. Then at night move the eggs and then place momma in the kennel on top of the eggs. Close kennel.
Depending upon your hen, you may want to cover the kennel with a towel for the next day - to help keep her calm when she notices she is some place "new". Some hens freak out and will leave the eggs, some worry for a bit but settle back down and some are so serious about brooding that they never even notice they were moved.
I keep food and water for mom in the kennel, within reach for her and make sure she gets out once a day to go potty. Usually when I am out in the coop - gathering eggs and cleaning, I just pull the broody out and put her outside. Sometimes she will sit in the same spot the whole time, other times she will run around - dust bathe - bathroom - maybe chase some chickens and then be ready to go back.