So many good ideas and observations above!
My experience has been that many people really enjoy teaching the kids once they get involved, and discover so much themselves through teaching, including getting closer to God and scripture.
The fear the regular church-goer feels is that they will not know enough Bible and will be embarrassed in front of the kids, so we help them understand that it's okay to say "I don't know the full answer to that, what do you think?" I tell them that teaching is a great way to discover more about the Bible and discover or exercise their various creative talents --whether it's showing a video, leading a discussion or game, or doing art with the kids. The workshops of the Rotation Model give them many ways to discover their gifts.
We do a spiritual gifts assessment in worship one Sunday every year. This helps me find people who have the gifts that might make them interested in teaching. I try to recruit 3 or 4 new teachers each year but I have teachers who have taught for 10 years and still love doing it! This gives flexibility.
With new teachers, I team teach with them or ask a seasoned teacher to do so. It is my experience that someone needs to teach with a seasoned teacher at least one full month in a row or at least 2 weeks one month and 2 weeks the very next month to really learn what to do. With the big screen and computer system we use for song worship and other workshops such as computers, movie theater, etc. someone needs to learn how to use all of those systems and be comfortable with them so they can focus on the kids and the lesson material. (Kids are a wonderful resource when teachers get stumped on media though!)
Most people want to be asked in person to volunteer for any ministry. That being said, once they have been personally asked and trained most are willing to continue to serve and sign up on their own - with a little prodding!
We have used Signup.com to have volunteers pick the dated commitments we need volunteers for. You can set up your Kids worship times and list the number of teachers, shepherds you need. I send a link to our signup.com page to our volunteers and they sign up for the weeks they are available to serve.
The site reminds them the week prior to their Sunday commitment which is really nice. I should add that we are not a small church, so signup.com makes our volunteer management easier on our leaders.
I have used this site for about 4 years now and it does take some of the burden off. I send group reminders through Signup.com when it is time to sign up for the next quarter and have many people that regularly sign up that way. There are always those who do not prefer that method. For them I text, email or at last resort call to fill spots that are not filled.
I hope some of this helps. I have learned so much from Rotation and the articles here!
