For the Target Debit card, all you need is a blank check. Think of their debit card as an electronic check card. When you swipe it and enter your pin it is just as if you wrote out a check. Takes a day or two to clear your account just like a check would, but no physical paper. Take a blank check into a Target, visit their service desk and tell them you want the Target DEBIT (not red) card. They'll have you fill out a short form that takes your in mailing address, etc. They'll run your check through the register. That reads the routing number and account number then voids the check. They'll give you a temporary number that you can use until your card arrives in the mail. Using the card, you immediately save 5% on everything in the store, including your no-contract phones, top-up cards and even your contract phones. The next thing to do if you can, is when they have sales on their top-up cards, buy several. Periodically, they'll have sales where you save $2-3 dollars per card.
EDIT: The other thing to do is get a job there. Even part-time employees get a 10% discount when using cash or a Target card (see above). And yes you still get the 5% on top of your 10% employee discount.