Hi M.!
There are so many moms clubs and playgroups in HB just waiting for you to join! My advice to you is to go to several and see who you click with and see how they work. Some are more structured and organized and others are more loose. I belong to two and am the leader of the Infant/toddler group (AKA the "Blue" group) of the HB South MOMS Club, which is a chapter of the International MOMS Club (www.momsclub.org as someone has noted below). The Infant/toddler group is for little ones zero to about 2ish. I joined when my son was two months old. In addition to weekly playgroups, we have a Mom's Night Out once a month and activities we do to support our local charity (a shelter for abused women and their children). There are lots of other activities, too. Feel free to contact me if you have any questions.
Another fun thing to do is to take classes in the Sands catalog through the City of HB. They have infant classes and they're affordable.
I was new to Huntington Beach when I had my son and I didn't have any friends here at all. Joining the MOMS Club (as well as the other one I am involved in--the Pacific Coast Mom's Club) was absolutely the best thing I did. It opened up a whole world of child-oriented activities and I've made some really great friends now!
Congratulations on your new baby and I hope to meet you soon!
~Lori