Go to your local bike shop and ask if they have any cardboard bike boxes spare, they usually chuck these out at the end of most days.
Depending on the size of box you get you might need to take a wheel off, take the front off.
Take your handlebars/stem off but leave brake levers on. Put handlebar/stem assembly beside the bike when you put it in the box.
You might want to take the forks off too, remember to zip tie, or a bit of string, through the head tube to avoid parts of the headset and spacers to get loose.
Pedals off, wrap these up and remember to put them in the box before you tape it up.
Once everything is inside the box you might need to add padding, so get any spare packaging, might be worth asking for two boxes from the bike shop, and pad it up.