If you are on regular birth control pills, you will get your period every month. However, it is safe to just skip your placebo pills and continue taking a new pack of pills (active ones) if you want to skip your period for any given month. I've done it a few times when I had to travel and I didn't have any side effects.
You still have periods every month when you are on the pill. You don't actually ovulate and have a period. But you bleed every month.
Taking the [combination] birth control pill stops your menstrual periods, for the entire time you use the pill. So, if you take the pill for 5 years, you don't have menstrual periods for 5 years.
The monthly bleeding episode pill users have is a fake period (withdrawal bleeding). The fake period is a "designer" bleeding. There's no medical/health reason for it; rather it was built-in to make pill use more acceptable to women/politicians/religious leaders of the time. How often you get a fake period depends on the pill regimen you use. For example, on the regular 3 weeks on active pills/1 week on placebo pills, you have a monthly fake period. On a 6 weeks on/1 weeks off, you have a fake period every 6 weeks, etc.