There are several apps that can work with the reminder app on your iPhone so this is a pretty easy thing to do. First, open the reminder app on your iPhone and create a new list called grocery. Then, any time you want to add to that list, you can use Siri in your watch and raise your wrist and say "hey Siri - add apples to my grocery list" and lower your wrist. No need to wait for Siri to actually finish.
This will add apples to the reminder list called grocery.
On the watch, you can use Reminder Nano to list the items, you can use App Things (my favorite) to have every item show up on a list on your watch - just like a to do list. You can then pick up apples and raise your wrist and hit the complication and check off apples.
Things allows you to sync to any list in reminders. So you could sync the grocery list.
There are other apps like fantastical that lists all your reminders at the top of the current day.