It is different with each woman. It could take just one month or a year. It also depends on the number of years you had been on the pill. You should just keep trying and give your body some time.
Depending on your age you will need to be off of birth control from three months to nine months before you are able to become pregnant. There is nothing stopping you from trying, however it may take up to nine months to become pregnant.
You can conceive in the next menstrual cycle after you stop taking birth control pills. Thus you could conceive as little as 2 weeks after the period from your last pack. There are no side effects this soon.