Here are what I found to be basic ideas for organizing play groups. This is based on my own personal play group experiences with my daughter. Take what you like and leave the rest. I also base some of what I write on my experience as a social worker prior to having my child. My 10 years in the field consisted of working with moms and young children and then later doing family therapy with adults and children of all ages.
To get started with a play group you only need 2 moms and 2 kids. You can add more moms and kids as you meet more moms and kids but don't let the lack of numbers stop you from forging connections for yourself and your children.
Ideal number of moms
I think that an ideal number of moms who come regularly is 5 or 6 and of course their children if you are looking for an intimate group. With this number or less, the whole group can bond. When 1 or 2 moms can't make it one week, there are still 3 or 4 moms who can. Plus, 5 or 6 different moms with children is a manageable number but enough to keep the group interesting. With many more moms, there will probably be more subgrouping, or rather, moms breaking off into smaller groups to talk. The benefit of a larger group is that you have a greater chance of finding more moms with whom you have things in common. The disadvantage is that unless there is a highly organized member in the large group willing to take a leadership role and do the organizing, the group may eventually fall apart.
Ages of children
I think it's ideal to have at least 1 child in your play group within 6 months of age to your child if your child is under age 3 because of the dramatic developmental phases of infants and toddlers. I don't think that you need to have all the children within a 6 month age range because a variety in ages means that the younger kids have older kids to learn from and the older kids have younger kids to teach.
Ages of moms
If you're within 5 years of age to other moms and your kids are similar ages, you have a good chance of hitting it off. If you have a lot in common with the other mom, 10 years age difference or less also could easily work. Just don't limit yourself from experimenting with making connections by automatically ruling moms out because of the age difference.
How often to meet
I think that once a week is ideal if you have the luxury of time. Every two weeks would be okay too. I don't think that once a month gives very young kids enough opportunity to remember each other from one time to the next nor does it give moms the regular contact they need in order to forge supportive relationships with each other.
Where to meet
At the beginning of the establishment of a play group, assuming that you have reason to believe that you and your child will be safe, I think that it's nice to meet at each other's houses. It's a confined area for roving kids which means that you have more of an opportunity to actually begin and almost finish a sentence which is helpful when first getting to know someone. Plus, there's a coziness associated with meeting at someone's house. Once you know each other a bit, then it's fun to branch out and meet in the park, or museum, etc. I suggest that you consider each bringing your own lunch/snacks so that the mom who is hosting doesn't feel pressured to entertain.
Organizing time for play groups
I suggest that you set up a regular day and time to meet when possible. When needed, you as a group can decide to change to another day and time as schedules of both adults and children shift. Having a regular day and time just takes some of the work out of organizing the group and goodness knows none of us wants to add more work into our day. The mom who is hosting the group can be responsible for sending out e-mails or calling group members if needed. If meeting in places other than a home, just rotate responsibility for this organizing.
Adding play group members
In intimate play groups, groups of less than 8 moms, I believe that it is best to add no more than 1 or 2 new members at a time once your primary group has been established. Hopefully you've established some intimacy as a group and don't want to feel completely invaded by the new members. Even one new member will change the group culture. At the same time, it is fun and exciting to welcome a new play group mom and her child/ren. Moms are about the friendliest group of people there are and want to share support with other moms. If your group is large, then adding multiple new members will probably have less of an impact on the group members.
Handling children's aggressive behaviors in play group
Certainly a mutually agreed upon rule should be no physical aggression allowed such as hitting, pushing, and biting. At the same time, all children are aggressive at times and this is normal. Most moms put a stop to aggressive behavior right away. If a mom doesn't take such behavior from her child seriously, then it may be helpful for her to hear from you (in a nice way, of course) that you do take it seriously. Every mom needs to be responsible for disciplining her own child unless you are very, very good friends with each other.
Keeping your mom friends
Even though you know that your child is the smartest, cutest, most talented child in the world, be careful about how you share this information with other moms.