Well if you still have the phone then you can connect it to a computer via USB cord and copy/move all the files you need (photos, videos, music, contacts, etc. just not apps) over to an empty folder on the computer. Then disconnect that old phone from the computer.
Next connect the new phone to the computer they same way (via USB cord) and you can copy all the files from the computer over to the new phone.
I would recommend leaving a copy of the files on the computer though, as a back up.