Join an organization or club with people who have common interests. You don't necessarily need to have a lot of common interests with people in order to make friends with them. In fact, some of the most rewarding friendships are between two people who don't have much in common at all, but if you like a specific topic, try searching for just a location. It's a great way to meet new local people! Social networking sites such as Facebook, Twitter and Google+ are great way to meet new people and learn more about the people you meet. A church, Masjid (mosque), temple or other house of worship is a great place to start since you have at least have a religious faith in common.
Join a sports team. A common misconception about this is that you have to be really good at playing a particular sport in order to make friends with others on the team, but not all teams are so competitive. As long as you enjoy the sport and support your teammates, joining a local team with a laid-back attitude could be a great way to make new friends. But a sports team isn't the only way. If you play instruments or sing, try joining a band or choir.
Ask them out for lunch or coffee. That will give you a better opportunity to talk and get to know each other a little bit better. A good way to extend yourself is to say: "Hey, well, I've got to go, but if you ever want to talk over lunch or coffee or anything like that, let me give you my number/e-mail address." This gives the person the opportunity to contact you; they may or may not give you their information in return, but that's fine. Maybe they don't have time for new friends—don't take it personally! Just offer your contact info to whoever seems to be potentially a good friend, and eventually somebody will get in touch.