To invite others to collaborate on a list, all you have to do is create or navigate to the list in question, click on the "+ Invite" button and invite whoever you want. Once people are invited, they will be able to add and remove items from the list, as well as receive notifications on updates and communicate on the list. And to avoid confusion over duplicate purchases, once someone buys an item on a collaborative list, it will be moved from an "Unpurchased" tab to a "Purchased" tab.
It's a feature people have been wanting for some time now, so it's nice that Amazon has rolled it out to everyone. It's especially useful for people planning a group event, vacation or other activity.