Well, coming into the wintertime, you usually need an insulated inner box or a box with tight fitting styrofoam panels. One of the best things to do is to check around with your local pet shops and ask them if they'll save you their boxes, or if you can have them on fish delivery day. Pharmacies and medical offices also get in regular insulated styro shipping boxes for medicines that have to be kept cold, like insulin. You can even purchase these types of boxes with companies that supply shipping goods for restaurants or other perishable food merchants. Making them with your own panels is pretty easy though. You can buy the sheets of styro at hardware stores and big chain stores (wal-targmart, craft section).
There are some good resources in this thread for supplies like shipping bags, rubber bands, and fish tranquilizers like hypno and bag buddies. Bag buddies (made by Jungle Labs) are what I use. They're a small tablet that you put in each bag that has an ammonia neutralizer, oxygenator and fish tranquilizer all in one. Breather bags are also great for small to medium sized fish, because they allow carbon dioxide to escape while retaining the oxygen and water in the bag. You'll have to use larger and thicker bags for bigger fish, or fish with more spines (catfish, etc.). Heat and cold packs are also good things to use during the winter and summer months. Again, check the shipping suppliers posted earlier in the thread for those items.
The process is pretty simple. Ya scoop em, you bag em, you put in the bag buddy tablet and you either tie it shut or rubber band it shut. If it's a breather bag, I don't leave any oxygen space inside at all. If it's a regular 2 mil or 3 mil bag, 1/3 water to 2/3rds air. Place the bags in your styro lined shipping box and add some fill (packing peanuts, shredded newspaper, etc.) to keep them from jostling around. Add the heat or cold pack, put the lid on and seal the box.
Then you mail it. You can use any of the shipping companies to send them (USPS, fedex, UPS) and they have rate calculators on their websites based on weight, the type of shipping (expedited, overnight) and from which zip code to where.