Hi Karin!
Correct. The easiest method is to bring cash for gratuities, which is about 18% per meal check. If everyone is under the same Dining Plan, then the waiter will apply the meal totals against one card, subtracting the credits for everyone. They will then give you a receipt with remaining credits listed.
You can put the gratuity in when they pick up the check, or leave it after they bring your Dining Card back. I try to get in the habit of giving the gratuity to them as I give the Dining Card, to make sure they have it, but either way you prefer should be fine.
Just a few notes: if you are a party of 6 or more, the gratuity will already be built in the bill. You don't want to "double tip," unless you were incredibly impressed with the service!
Good Luck on your trip to the States and visit to Disney World!