The best way of course, is word of mouth. So, when you are out shopping or taking a walk in the local park, go up to other moms and ask them whether there are any mother’s groups in your area that you could get involved in. Then of course, there is always the Internet. Take a little time and have a look online as well - you never know what you will find there.
Once you have done your homework and have a list of groups that you are interested in, visit them one by one until you find the one that you feel most comfortable with.
Most mothers’ groups meet during the day each week. This is fine for those stay-at-home moms or moms on maternity leave, but for moms who work full time, this could pose a problem. If you work full time, then do not give up - keep asking around.