Lots of non-profit organizations need volunteers--food shelves, animal shelters, Habitat for Humanity, etc. Serving your community will give you an easy way to meet new people with similar interests.
Any group about anything you're interested in is a good way to meet people. If you're in school check out the clubs in the school, if not you could volunteer your time somewhere like at a hospital or get involved in your local church. All great ways to meet people.
A good way to meet people is to take classes or volunteer at something that is of some interest to you: animal welfare, a political candidate or a zoo, library etc. Then you will have something in common right from the start.
I think church is safest way to go. They have lots of different age groups and socials to meet people. You can find who you relate to best and then do stuff on your own with those who you feel you want to get closer to. Civic organizations too.