It depends on the hen. Some will stay broody all season. Others will sit for 2 months on golf balls. Some will only be half broody, and leave the nest at night to go roost.
When they have chicks, they'll usually get bored with them around 7 weeks of age. If you take the chicks too early, they may try again.
I had one who went broody in June. I let her have duck eggs for awhile, then gave those to a broody duck. Bought her some chicks. She raised them, then after 10 weeks, she turned around and went broody again. A half hearted attempt, she gave up after 3 weeks when I didn't keep any eggs in the coop for her. Then she went into her first big molt, now she's finally back to laying again.
I've had some get so serious about it they would steal eggs and find something, anything, to sit on. And they would do that from April until September. Those were Bantam Old English.
A Black Rosecomb Bantam hen, she was my "most broody". Stealing eggs and chicks, no nonsense about it, she was a brutal broody. She met a hawk in the air protecting a batch of chicks, and that was the end of her. She was a neat chicken. A little crazy, but neat.
Then some others... they'd last about 3 weeks or so, then never tried again. You never can tell what a hen will do, until she does it enough to let you know how she is.
None of my others in the current flock go broody, just the one Wheaten Marans. The others accepted her chicks fine, no drama. If a broody hen has good flock standing, and isn't low bird on the totem pole, giving purchased chicks to the broody is a good way to introduce new birds. They need to be less than a week old, and spend about 3 weeks in a "broody hut". Then allow the rest of the flock to meet them, and if it goes well, they can be added to the main coop earlier than if they didn't have a mother to "introduce" them to the flock.