Ive tried many apps for making & live sharing of lists. None beat AnyList. My wife and I use AnyList with great ease to share a grocery list, packing lists, travel planning lists and gift wish lists for the kids. Its fantastic.
AnyList has loads of great features, is regularly being updated and is backed by friendly, prompt support. You cant go wrong with this app.
Beil about AnyList: Grocery Shopping List, v5.5.5