So I can physically put the disk in my paper tray to my printer and it will print on the disk?
Depending on your printer I would not recommend doing that. Discs are somewhat stiffer then paper...
That out of the way, if your printer is capable/compatible with printing directly on a disc, there should be instructions on how to proceed in its manual. Printable Bluray/DVD/CDs have been around for quite a while, so they're reasonably well supported. You'll also need some kind of software for label design. Nero used to be able to do this, but I haven't used it in ages. Keep in mind, laser printers cannot do this.