I currently have 6 broody hens. This is down from a dozen. Five of the 6 are related, so you have to figure they have very, very broody backgrounds.
Here's how it happens at my place:
I notice that a hen is laying more than usual. Like a dozen eggs without taking a day off. I know at that point that she's laying her clutch and getting geared up to brood. So I then watch for her to go broody. If I don't want any chicks, I put her in broody jail. It takes 3 days to a week to break her of her broodiness. I then let her out. About a week after that, she starts laying again. Normal egglaying schedule for about a month, then the whole cycle repeats itself.
If I do want chicks, it's a little different. I notice that she's laying more than usual, so I start thinking about where to get hatching eggs. When she goes broody, I move her to a broody house and lock her in for a few days so she will decide that she can brood on that nest and not the one she originally chose. By that time, my eggs have arrived. She sits on them for 21 days, hatches babies, and mothers them for 4 to 8 weeks. Then she starts laying again, and is broody again in about a month.
This goes on all spring and summer long, into the fall. I decided to hatch eggs in autumn this year. I used 3 broody hens, my faves, and interestingly enough, none show any signs of wanting to wean the babies. One hatch is 10 weeks old, the other (with 2 mommas) is almost 8 weeks old. I'm thinking that they are still mothering the babies so well because they aren't ready to lay any more eggs due to the seasonal change.