The San Francisco Bicycle Coalition and the New Wheel bike shop (Located in San Francisco, Marin, and here in Oakland.. soon!) put on a webinar a little while ago that covers an introduction to biking with children. It has a bunch of useful information, especially for those who may be new to biking or new to riding their with children.
Karen from the New Wheel spoke about the benefits of family cycling (it's joyful, flexible, fun, and empowering) and how improving city infrastructure has made this easier than before. Electric motors and improvements in battery technology have made it possible for e-bikes to serve as a lower-carbon and more fun minivan replacement.
She talked about different ways to carry kids (trailers, trail-a-bikes, family bikes and cargo bikes, front and rear seats, having kids ride their own children's bike) and common concerns, such as safety, feeling comfortable on a bike, loading kids, and locking/parking. And she talks about common accessories, such as helmets, lights (don't forget to get lights for you and children's bike lights too!), kickstands and snack bags. I can personally vouch for the snack bags. Bags are also really useful for helping your child carry rocks, sticks, band-aids, and other things that they may want to pack or collect during your travels.
Karen's talk in the video below is an excellent and comprehensive summary of why riding bikes with children is great, what concerns parents may have, what the current offering of bikes and options are, how best to get started, and how to ride in the city.