How many fish are you shipping?
Unless you are shipping A LOT of fish, you don't want to ship in a styro from the LFS. It'll break your piggy bank. They're bigger than 12" on a side, so you pay for the volume you use, as well as the weight. You'll pay $30 or more to ship it empty.
What you want to do is get some styrofoam sheets and line the inside of a regular box for a smaller shipment. You can buy them at home depot for insulation. Cut them so they're tight, and they work just as good. Heck, even if they're not a super tight fit, they work just as well -- I'm pretty sloppy with my cuts. You can also fill the box with peanuts to add extra insulation. (Tony, put the jar of planters down, that's NOT what I meant by peanuts).
You can get bags at your LFS, or order breather bags, which are great for MOST fish (except anabantoids). Most stores will give you a bag or two, but either buy something while you're there, or give them a couple of bucks for the bags; bags do cost money, and it adds up.
Double bag your fish.
Double bag your fish.
And while you're at it, you might want to consider double bagging your fish.
Don't use a cold pack. Unless you're shipping a very large box, chances are it'll rest against a bag and make that bag very cold. Cold packs are for larger boxes, not smaller.
(I'm assuming you're sending someone like 3 fish or something).
Bag with as much air as possible. I don't use pure oxygen, as I have never seen any significant benefit for most properly bagged fish with it. Okay, you're shipping a bag with 200 fish in it, or 6 12" koi, or something like that, yes, it helps... but shipping a bag with a reasonable number and size of fish? Makes no difference.
Or, if you're really intimidated, give your fish to a professional shipper to do it for you. I suggest Batfish Aquatics.