Not only will your local bike shop have quality 'virgin rainforest grade' cardboard boxes going spare they will also have the plastic braces that fit inside the front fork, the plastic plug to fit into the top of the seat tube, the plastic spacers to fit on the rear q/r and the foam 'pipe wrap' tubes that go around the three main triangles. They may even let you have a few zip ties that you can use to tightly bind the handlebars to wherever they fit in the box. The aim of the game is to not have anything that can fall from the bike or any paint that can be rubbed off, e.g. from the front hub knocking on the down tube.
Try to pay attention to the gears, if the chain is on the outer chainring and on the big sprocket then it is less likely that the rear mech or chainset will get damaged. As for the pedals, you may need to have some lightweight pedal spanner that actually works, or a big 6mm hex-wrench (if your pedals support it). Ideally you want nothing to rattle.
Bear in mind that boxes come in different sizes, you will most likely want the larger size as these boxes are fairly optimised - you won't get a 23" frame to fit into a box originally designed for a 17.5" frame.
If you are doing a cycle tour you can also use some of your clothing items, towel and other soft items to pad out the box. Get this right and you will have one big box and a manageable amount of hand luggage. Get it wrong and you will have a box that you can barely lift and the airline will not take.
Which brings me on to the next point. Not only do some of the 'proper' boxes cost a minor fortune, they can also weigh a metric tonne (or thereabouts). Hence the cardboard box has a lot going for it, not only is it disposable, it is light too.
Remember that baggage handlers will need handles for handling your baggage, use tape to strengthen the hand holes that are already in the box and tape up the top and bottom so there is no chance of your precious cargo bursting.
Before now I have re-assembled the bike in the airport and dumped the big cardboard box in one of their bins. On the return hop I have also managed to find a not-so-local bike shop, obtained a box and packaged accordingly for the journey home. This is less stressful than relying on the airline having a box. Negotiating the airport is always easy enough because they have little trolleys everywhere.
If you have travel insurance take pictures of your bike before departure and write down the frame number. Also make sure that the bike is completely clean as some countries do object to mud being 'smuggled in'.