You can take a bike on a plane, just like other luggage, but it must be packed either in a cardboard box or a special bag. I advise against cardboard– it is usually bigger and heavier than a bag. Furthermore, you have to look for another box before going back home. It has got one advantage though – offering better protection against mishandling of luggage at the airports. However, it is better to purchase a special bag. In order to pack a bike into the bag, you should remove the wheels, saddle, racks and handlebars. Next, you have to attach the wheels and other movable elements to the frame, using adhesive tape, for instance. Secure the frame against chipping or scratching by using thick fabric.
Important: deflate the tyres because low pressure in the cargo area may make them explode.
Below shown a way of packing bike into the bag.