How are you supposed to pack your bicycle when taking it as luggage on an airplane?

I have flown my bicycles without boxes on several occasions. Just remove the pedals, turn the handlebars sideways and rotate them down so the brakes levers are not protuding.

You can get a factory shipping box from your local bike shop and use that. Get a big one to have extra space and easier packing.

You can use a large heavy duty plastic bag. But I would prepare the bike the same way as my no box example.

Some airlines may still have cardboard boxes, but these are becoming rarer.

You can buy a bike case. They are not cheap and need to be stored during your ride. But they are sturdy.

You could buy a Bike Friday, which fits in a suitcase the the check-in agents won't know it is a bike.

There are many options for getting a box for your bike. It all depends on how much you want to pay. I did a quick google of Airline bicycle travel box and came up with choices ranging from cardboard boxes for $US40 to solid plastic travel cases for $US600

Also there are places like this company that will ship your bike for you and have tips and videos on how to pack your bike, and will also sell you packing materials.

Anecdotal, of course, but worked for me on my Warsaw - Sydney trip, where I brought two bikes (one road, one mountain).

I got 2 cardboard bike boxes from my local bike store (they throw them away - at least in my case - so you can get them free). They're fairly sturdy, definitely more solid then your typical cardboard box. In order to fit the bikes into boxes, I needed to take the wheels, saddles, forks and handlebars off. Didn't need to unscrew brakes - just needed to realign the handlebars to a more vertical position.

I bought foam pipe insulation, cut it into pieces of fitting size and wrapped it around the frame elements (didn't wanna crack it - carbon, I think aluminum/steel might require less care), attaching it with cable ties. I also bought a whole lot of bubble wrap and triple-wrapped everything. Since I had limited luggage allowance, I didn't take a suitcase, instead i stuffed my clothes in with the bikes for even more protection ;)

Taped the boxes shut and wrapped them with plastic wrap.

The bikes weren't damaged, although the same cannot be said about boxes. One axle popped through one of the boxes (undamaged) and the plastic wrap was torn badly.

Naturally, your mileage may vary. Luggage handlers aren't particularly gentle.

Edit: One thing you may want to check first is the luggage size limit (not just weight). I flew Emirates, their rule is that the sum of dimensions of each piece of luggage cannot exceed 300 cm. As far as I remember, the boxes were something like 147x80x30, so they fit in with a bit of room to spare.

One answer suggests having it delivered. This greatly depends on your starting point and destination - I checked the pricing for a delivery from Poland to Sydney - would literally cost me more than flying back from Sydney, picking it up and flying to Sydney again. Can be very prohibitive.

It completely depends on the airline as to what they will accept. They are all different, there is no one universal answer. You also won't necessarily get a clear answer from them either, and what they say on their website may differ from the reality of what they actually accept at checkin. Arrive early and be prepared to argue and sign a liability waiver. Note most airlines want advance notice you have a bike. Note as well that in many cases the airline matters less than the airport, it's the airport that does the baggage handling after all.

It also depends on what type of bike it is. I have flown hundreds of times both with heavier duty touring bikes (steel/aluminium/titanium) and lightweight road bikes (carbon or titanium). My touring bikes I almost always fly with unpacked, IF the airline will accept them that way. MOST airlines will. Some you need to argue the point at checkin and sign a waiver. My road bikes I always put in a dedicated heavy-duty plastic bike box (B&W) which cost me hundreds of euros and is extremely heavy.

I am of the view that if you are packing the bike, you either do it properly or not at all. Like Tom says, an unpacked bike is substantially easier for baggage handlers to handle- they can (and do) wheel it about th place. A box converts that into an extremely large, extremely heavy and unweildy piece of luggage and they will handle it roughly. They will literally throw a box off the plane down onto the tarmac. They won't do that with a naked bike, honestly, they will lift it down. I have seen this with my own eyes again and again and again and although I have never had a bike damaged packed in the B&W box, I have had the actual BOX damaged badly, through abuse... because they will absolutely throw boxes around with abandon. I have NEVER had a naked bike damaged in this way.

As such, "wrapping in plastic" is IMO the absolute worst thing you can do. It gives zero actual protection to the bike, but it does convert the bike from an easy to handle object that can be wheeled to a large unwieldy object that can't.

It's advisable if you have big pedals to be able to take them off, but with SPDs, I just leave them on and put some foam on them so they don't damage anything else. I lower the saddle but to be honest that I think is optional. That's it, I literally cycle to the airport, lower the saddle with an allen key, stick some foam on the pedals and give the airline the bike, like this: http://i.imgur.com/jOxBuqf.jpg