It varies with each female. Some women will become pregnant the first cycle, others take up to 2 years. I'm assuming you had the Mirena, as it's the most commonly placed IUD. The way it works is that it thins the lining of your uterus, so it's in your best interest to wait a few cycles so it thickens up. Otherwise you risk miscarrying. It might also take a few cycles for your period to become regular again.
My friend had Mirena and got pregnant before she even had her first cycle