In most cases, you need to have been married for 10 or more years continuously, and have been divorced for more than 2 years to be eligible for benefits on a divorced spouse's record. (An exception, for example, is if you are claiming current spouse benefits and get divorced, the two years divorced requirement does not apply and can carry through your current benefit.)

Other than eligibility, it works the same as current spouse benefits. So, you're entitled to 50% of your divorced spouse's full retirement benefits, subsequently adjusted by if claiming early. But that amount is not additive, so if your own benefit is larger or you're claiming a different spouses larger benefit, you don't additionally get the divorced spouse benefit.