There are various ways to carry them, but one of the most important things is to make sure the ceramic inside the Egg is either padded, or removed and transported separately.
For our small Egg I made a stand out of 2x4's that doubled as a crate to carry it with. I don't have any pics of it as it wasn't the prettiest to look at but it was functional. I would pack the inside of the Egg with egg crate foam (ironic?) to keep the firebox and fire ring from moving too much.
EDIT: It looked something like this: