To send boxes from a post office they need to be blank boxes. You can find cardboard boxes at The Daiso (a 100 yen store), but they only have small or medium sized boxes. They might not be used to foreigners buying cardboard boxes, so if you want to be safe bring a picture of a cardboard box. Cardboard box in Japanese is bourubako (ボール箱) or danbourubako (段ボール箱).
The post office has a variety of box sizes from small to medium. You can also buy padded envelopes and regular envelopes. For boxes ask for bourubako (ボール箱). For padded envelopes as for kusshon fuutoo (クッション封筒).
If you are sending a padded envelope through ems make sure to get the ems padded envelope.
At the post office bring the package to the mail counter and they will help you with the label. The price will depend on the weight and which mail service you use. The slowest mail service can take a couple of month to go overseas and EMS is the fastest can take a week or less.