When my daughter used to depend on a bike for transport (just a year ago) she had a small wire 'trailer' sort of like the little basket carts you can pull behind you with laundry or groceries in them, but it could be hitched to her bicycle.
There is a wide selection of trailers available to hitch to your bike. Some of them are enclosed and helpful in rainy weather. Just go to Google images and type in bicycle trailers to see a selection of them.
You can also get sidecars that are useful for carrying objects as well as people (children). You can see them on Google Images too. Just type in bicycle sidecar.