Short answer
How does the shared shopping list work?
Every purchase is a task of the Purchase type, with an optional price, so the family's shopping list lives in the same planner as everything else.
Add a purchase in the iPhone app or on the TV. Give it a price if you know it: the phone takes dollars and cents, and the TV works in whole dollars. Leave it in the queue for someday, plan it onto a day, week or month, or give it to someone for today.
When the planner is showing purchases, a line at the top adds up what's planned for that day, week or month, such as “$118 planned · 1 without a price”. It counts every purchase planned in that window, bought or not.
A purchase given to someone lands in their list on the TV, next to their chores, and they tick it off when it's bought. The tick is saved to the family's shared list, so the iPhone app sees it too.

