Though I'm not very experienced in this, I have done it before and it went really well. Are you planning to give all three hens chicks?
The first thing you have to think about is your hen's positions in the pecking order. If they are low, there is a chance the other chickens will try to attack the babies. If this is the case, then you will have to set up a barrier between the mama hen and the other chickens. If they are at the top of the pecking order, the other chickens should not mess with the babies. My mama hen is the leader of my flock, so I didn't have to separate her.
Once you have figured this out, and made the appropriate adjustments, you can get the chicks. You should have food and water by the nest boxes so that the mother and the chicks can easily get at it.
To put the chicks under the mother, you have to wait until it is completely dark out. Take the chicks out to the coop, and gently remove the fake eggs from under the hen. It is extremely important that you do this with as little light as possible, and with as little noise as possible, so that you don't wake her.
Once the eggs are out, you pick up each chick one by one and put them underneath the mom. The chicks should immediately get quiet and the hen should spread herself out over them.
Do this to each one of the hens.
Once this is complete, close everything up and leave them alone.
Go back 10 minutes later and make sure that the chicks are still under mom, and the hen is asleep.
If all is well, return in 1 hour and check if the chicks are under her and the hen is asleep.
The next morning, wake up just as the sun is rising. If the hen rejects the chicks, she will either just get up and leave them in the cold, or she could attack them. It is really important that you are there so you can prevent any injuries.
When you go to the coop, the chicks should still be under the hen, but the hen should be awake. If she has accepted the chicks, she will be spread out on the nest and she should be constantly clucking gently to her chicks.
A little later in the morning, you should see the chicks walking around in the nest with the hen watching over them protectively. If you see that, then you know she has accepted them and she will raise them.