Early in my mommy-ing, I became friends w/ the women I saw every month at the LLL mtg I went to (there was also a weekly playgroup then). Later, when all their children were going to school & mine weren't, I became friends w/ other home educating parents. That's mostly my friend base at this point.
Other places where you might find others to socialize w/ are your local library (or another not-so-local library), meetup.com, a local arboretum that holds classes, the local YMCA, any place that holds mom & me kinds of classes (or classes for many aged children - music classes often cover a span of ages), Holistic Moms Network (they charge, but some feel it's worth it), etc.
If all else fails, start a group of your own. I've held group meetings in libraries (some charge, some do not), Panera bread (some have a separate room that you can reserve), local indoor play place (can be tricky, but can probably be done), churches, and that's all I can think of right now.
IT can be hard & nerve wracking! I've been there. I know it helped me in the past few years to not think that I needed a gaggle of friends RIGHT NOW. I tried to focus on building friendships w/ just one or two people at a time. Life is just too busy for anything more!
ETA: the tribal area here - post that you're looking for friends in your region of the world/country. How could I forget? Oh, yeah, mommy brain.