I can relate to your situation. Interestingly, the Tampa Times today featured an article on this very topic. They mentioned two books: MWF seeking BFF and The Friendship Crisis. The first book sounded particularly interesting because it chronicled a woman's quest to do exactly what you want to do.
I'm thinking your child/children are still in elem school so playdates are particularly helpful. Once they get older, you won't really have playdates and parents will tend to just drop off their kids which doesn't leave much time for chatting. I remember doing things like meeting a mom and kid at the park after school or connecting for lunch on half days when my son was this age. My son was very active in Cub Scouts and the parents were required to stay for the meetings. We met at a church so while the kids were in the classrooms, we were in the fellowship hall chatting. We also went on campouts together and that's where we really bonded. I made some great friends there.
I'm a fan of a business etiquette writer named Ann Marie Sabath. I heard her speak once and she told stories about how she would talk to people wherever she was. She would meet with most interesting people this way. It will help with your small talk skills. This was before everyone was always looking at their cell phones, but I do try to do this myself.
In my situation, I know a lot of people, but sometimes don't feel like I'd be included if there was a party or something like that. I'm not really in a circle of friends, and I really miss that. I have a few people I call to get together for lunch. I'm trying to organize girls nights out. So far, the Boy Scout moms have done one and we've done two with the women at my job. I used to do these with a group from my son's school but we have all gone our separate ways. I've also trying to get active in my sorority's alumnae chapter.
I think in the end, you just have to be confident, interested in other people, etc. When you are going somewhere where you will be around people, make sure to read up on the news of the day, wear some interesting piece of jewelry that people will notice, and just be honest. I was at a function recently and just walked up to people and said "I'm new here." I think it helped.