The credits are stored on your room key that also serves as your ticket. You can use the credits up all in one day or spread them out. It is up to you. They do separate kids and adults credits, so if your kid wants an adult meal, you might have to pay out of pocket. This does take some planning especially for table service since it is really hard to just walk up and get in any more.
The cost of a meal is not factored into the credits. Like the poster before, you get 1 table service, 1 counter service and 1 snack, per person, per night you stay in the hotel (not # of days on the tickets). At table service restaurants, your server will usually ask if you are on the dining plan before you order and they can help out.
Table service you can order: 1 appetizer, 1 entree, 1 dessert, and one non-alcholic beverage - if character meal it is usually pre-selected or a buffet.
Counter service you can order: 1 meal (sandwich/fries, pizza, etc.), dessert (usually chocolate cake, carrot cake, etc) and 1 non-alcholic beverage
Snack is anything under $4 - usually on the menu's it has a DP icon next to it to denote you can have it as a snack.
I usually plan out our TS right away and let the others fall into place when I get there. Every receipt you get has the number of credits left, so keep a tab on that. By half way through the trip you will know if you are running short or if you have enough to enjoy more.
Our last day of our last trip we had 2 Counter Service and 2 Snacks left. I hit Casey's Corner for the CS and my husband got the girls popcorn for the snacks. We ate them on the monorail heading back for DME.
DS is nice, but does take some planning to get all you can out of it.