In order to meet a variety of people, you have to put yourself in situations that are slightly uncomfortable for you. For example, if you are someone that enjoys physical activities like running or biking, opt for something that stretches your mind, like a book group or lecture. Do you like "girly" things, like sewing or baking? How about taking a class in something very "ungirly-like" and see if you meet people that draw your interest.
The key to meeting people in these types of situations is to have a sense of humor. You will feel a bit awkward and out of the place, and that's the point. Don't fight it. Instead, laugh off any nervousness and look to the people around you to help you adjust. These are the folks you'll likely connect with.
The more people you know in general, the better you'll be at having an eclectic group of friends. One of the easiest places to meet a large group of different people is the Internet. If you browse websites that can help you meet people, you may find a few pals that you can turn into real-life friends. Even if you are not able to meet online friends in person, you can still benefit from their varying opinions and attitudes.
If you want friends who are different from you, start with a mentor. Mentors generally are similar enough to you that you get along well with them, but different enough where they can share their opinions and experience. Your mentor might encourage you to hang out in new places or introduce you to their friends. All of this is good for expanding your social circle to include a more diverse group of people.
When it comes to finding new friends, consider breaking the standard rules of small talk and chat up some folks who share a different opinion in subjects that are usually taboo, like religion and politics. Rather than trying to change the person's mind, converse with the goal of trying to understand exactly where they are coming from.
This exercise isn't to change your mind or opinions. Rather, you'll meet people that have a completely different viewpoint. Once you agree to disagree, you can get to know each other on a more personal basis. These are people that you would normally overlook when it comes to friendship, which makes engaging them all the more important to growing a diverse base of friends.
Want more ideas? Sign up for my free ecourse, 101 Ways to Have More Friends.