years ago, i used to rely on the airline-provided cardboard box. then i learned of these great hard plastic shell cases with foam padding, wheels, etc.. now that is all i use.
you have to break your bike down (wheels off, seat off, handlebars off, rear derailleur off, etc.) but it unless the airlines drop it at 10,000', your bike will arrive in 1 piece.
they cost between $200 - $1,500 depending on how fancy you go. mine was a $250 Serfas case that has served me well for many years and many trips, including flights to Europe.
depending on the airline, you'll be charged between $15 - $75 each way for an oversized bag fee. but the same charge PLUS a box fee would be charged if you went the airline-provided cardboard box.
