My daughter has been on this, "PLEASE, can we get a dog?" kick for a few months now. I wish I could say, "Sure, c'mon lets go get one!", but little does she understand, dogs have a lot of needs! Here's a basic checklist of things you'll need to have before bringing the new family member home.
Feeding: You need to make sure you have food and water bowls, along with food. I would also suggest buying a bin or bucket to keep the food in. This way, you can buy large bags of food at a discount and make sure it stays fresh. Treats are good to have on hand, especially for training purposes.
Safety: Not only is this a law in many states, but having your dog on a leash with a collar when taking walks is very important for safety reasons. Dog collars come in a variety of sizes, so make sure you have one that fits your dog. Don't forget to get an ID tag with your contact info in case your dog gets out of the yard!
Health: You should try to find a veterinarian before you bring your dog home, or soon after. Dogs need several vaccinations in puppyhood, and please don't neglect to have him or her spayed or neutered! I would consider buying flea (and tick) prevention products. Dogs are bound to pick these critters up and it is much easier to prevent infestation than to get rid of it! Make sure you read the directions as a lot these products can't be used on small puppies.
Comfort: Puppies are playful and active, so you'll need quite a few toys to keep them happy. I would also consider buying a few dog beds; one for the general living area and one for the bedroom.
The products above are just basic necessities; there are many other things you'll want to get eventually.