How do you mail a package to Japan?

It is about 22lb. I need to know what kind of address information I need (if you have a format I can follow that would be perfect), and what service I should use. The faster the service the better. A friend recommended EMS. I am just shipping clothes to someone who lives there (it is their own clothes), would customs charge me anything? Also they do not have a PO BOX, they just have an apartment number, street name, city, and zip code, is that sufficient?

Check out the mailing or package forwarding system in your own country. Nobody can help as you don't even say where you are sending from.

I will be sending this package from the Bahamas to Kagoshima Japan.

Please ask at your local post office. Different postal services of different countries have different fees and weight or size limits on packages going overseas using certain mode of transport.
EMS or its equivalent will be very expensive for sending something like 10kg of stuff.
The one who may get charged customs duty is the recipient, not you. You need to declare it as "personal effects" and write "used goods" to avoid the recipient imposed import duties.
No PO box is required, but for express service you might need the recipient's phone number. But you need to check with your local post office.