Many airlines will carry bicycles for free as sports luggage, or add on a small supplement. To avoid unpleasant surprises, tell the airline beforehand that you’ll be taking your bike with you and make sure you have the terms confirmed to you in writing.
You should also think about additional luggage insurance. Some airlines exclude liability for sporting equipment altogether, or only accept liability for a sum that amounts to less than the value of expensive bicycles.

Bicycle cases or transport boxes can be used to protect bikes against damage. Bicycle cases with hard outers offer the best protection, but are more expensive to buy. Check the classified ads in the appropriate cycling magazines and you may well find companies offering the rental of bicycle cases. One low-priced alternative is transport boxes that can be equipped with tension belts and rolls (e.g. as available by mail order from Rose Versand, Germany) or used delivery boxes that can mostly be obtained from cycle stores for free.