No matter how long you have been off of them, you need to wait 3 months to reasonably expect your birth control pills to act as reliable protection. Consult with your OB-GYN to be sure.
It depends on the kind of birth control, however the only safe assumption here is to assume that it will take the same amount of time as starting from scratch. Ask a doctor to make sure and be careful.
Depending on the particular pill, a minimum of 7 days up to a full Month. Safer to figure the full month and use extra protection during that time. Don't consider previously taking them as a factor in the current situation.
If you are talking about traditional birth control pills, then it doesn't matter how long you have been off of them or how long you were on them before. Read the packet and it will tell you how many days before they are effective, which is usually seven days.
Most doctors will tell you that to be safe and to ensure that you do not have an unwanted pregnancy that you need to be on birth control for at least 30 days or one menstrual cycle prior to having unprotected sex.