iOS: When it's working properly, Passbook should automatically update all the cards you have stored in it, but it doesn't always work as described. If you're standing in the checkout line and need to make the card refresh right now, Cult of Mac shares a tip for doing just that.
The Passbook app has a "pull to refresh" option built into it, but it's a little hidden away. First off, open up Passbook and select the card you want to refresh. Then tap the small "i" icon in the bottom right corner. The card will flip over. Here, just pull down from the top of the screen and it'll refresh. If that card is refusing to update when you're trying to buy something, this is just the trick you need to make it happen.
Manually Refresh Items and Passes in Passbook [Cult of Mac]