You can't really travel with your turtle like you would with your dog, but there are ways of safely transporting your snapper from one place to another. Taking it with you in your car is quite simple - it could be just a cardboard box for smaller turtles. For bigger I suggest something more sturdy, like a large plastic container (you would have to make air holes in it) or small animal carrier like those for cats.

The turtle should be placed in a cotton bag, like an old pillow case, and secured with rope. This will reduce the stress and prevent the turtle from trying to escape. Next step is to get ready with a number of sheets of old newspaper. Squash them into balls and tack around the turtle after its being placed in the box - this will prevent the animal from sliding and bouncing. (instead of newspaper styrofoam chips are also great for this purpose)

There should be an extra layer or two of cardboard placed on the buttom of the box - snappers are powerful and their claws might damage the base of the box easily when trying to move. The last thing is to close the lid and secure it with tape.

One word of coution - don't place a wet towel inside the box! This will just make the turtle cold and if leaked make the box weak.

For winter times or long distance transportation, like on planes, things get a little more complex. The box with the turtle should be placed in another larger box. This bigger box should be large enough that there would be few inches of space between the two - the bigger tha gap the more stable the temperature will be inside. Fill this space with newspaper balls and place a heating pad on the bottom and a couple on the sides. After placing more newspaper cover the box containing the turtle, close the box and after cutting a couple of air holes (this would be sufficient - too many holes will destabilize the temperature inside) secure it with tape.

If sending the turtle by air make sure to indicate with arrows the top and make a clearly visible note warning that the package contains live animals.

How to prepare the turtle for the trip?

The turtle should not be fed before the travel takes place. A good idea is to place it in clean, fresh and warm water to give it a chance to defecate. Before putting the turtle in the cotton bag it should be dried with towel and left outside for a short time to make sure it is not wet. Most turtles will 'pee' after being taken out of water - if that want happen you might end up with the whole set up soaked and useless, so make sure to give the animal some time to move around.

If exporting your turtle to another country, or perhabs even within the same country, a good idea is to have the turtle checked by a vet who should write a note stating that the animal is healthy and safe for the trip, and that the 24 or so hours without water will not affect its health. Some countries require such statement from a recognized animal doctor.

Before sending the turtle make arrangements with a shipping company. You can't just make it ready and take to to the post office - they will not accept it. Of course, don't take your chances trying to disguise it as regular mail - it might kill the turtle and give you lots of trouble. Double check if any importation permits are required and make sure to attach all the paperwork with the package. Also check local laws - some places ban snapping turtles all together, and if sending another species make sure it is not on the list of the endangered animals.

After the trip place the turtle in warm water - it will be a bit dehydrated and might even float for a short time, but it will get back to it's normal self in no time. Snappers, and other water turtles, spend periods of time without water when moving from one place to another or searching for a spot to lay eggs, and a day or two in a box will not harm them.