Do a backup of your 4, either to the cloud or your computer, depending on how you usually do this.
If you backed up your 4 to the computer, connect the new phone to the computer at this point, if you restored it to the cloud, do NOT connect it to the computer (or you might get an old backup by mistake). Just connect it to a charger.
When you first power up your new phone, it will ask you whether you want do configure it as a new phone or to restore it from a backup. Select "from a backup". The prodedure is slightly different for computer and iCloud backups, but you'll be able to figure it out.
This will restore all your apps, settings, and camera roll. Then you can either sync it to the computer or redownload your music and movies (depending on how you manage these things).
Once this is done, you can delete everything you don't want from the old phone.