If you have a person or two who is experienced at running meetings and facilitating this kind of thing, great! It's helpful to have someone drawing up the agendas, identifying topics, keeping the conversation gently moving along, including people who aren't as good at speaking up, etc. Otherwise just put the hat on yourself and do your best, it will be fine. (I usually asked one person to come early each week to pair with me in drawing up the agenda.)
This is the trickiest part. You want at least 6 people, no more than 10 people each week, and you want to find people who are actively trying to level up in their careers right now. And you want a balance of genders, experience levels, and perspectives, and to exclude multiple people who work together. It's hard!
Decide if there is a particular theme to your invitations or not (managers only? women only?) and then do your best. Consider opening it up to referrals from others. Otherwise you will know everyone and no one else will, and it's nice to be on a level footing.
I can't recommend enough the decision to meet in someone's home, on a weekend. You want to be chill and relaxed, not dragging the sorrows of the workday on your back. Create a google group or a facebook group where you can all communicate.
This is the toughest part, so have someone bring donuts.
It is going to be awkward. Oh, so awkward. Acknowledge the inherent goofiness of the situation and move along. Tell everyone ahead of time what to expect, and about the homework.
You'll want to start with an opening circle, promptly at the start time. Have everyone introduce themselves to the group, and state an intention for what they hope to get out of the next 6 weeks. Ask questions. This is a conversation, not a performance.v