One key tip: Do not let your busyness get in the way of bringing in those new volunteers. Do whatever it takes right away to say yes to (or to find a job for) every new parent who asks to help. Connecting with them and welcoming them now is the most important thing you can do these days for the long-term health of your group.
If you delay -- or worse, say no -- those new parents will think you don't want their help. Their enthusiasm will wane. The clique word will creep in even when it's not your intention. Ugh.
I love this article about little things PTOs and PTAs do that hurt involvement. Saying "not yet" to willing volunteers is at the top of that list.