It is usually as easy as
n2gun said except without having to mess with BIOS. If the computer is detecting the CD-ROM on the secondary it will likely pick up the burner when you install it. Bios setups can vary, but dont mess with it until you are sure it isnt going to show up on its own.
There is no reason to not keep both the CD-ROM and burner. Unless you have old equipment or old Via busses it is just as reliable and successful to copy directly from the CD-ROM to the burner. Your burner has buffer underrun protection.
Some computers come with a ribbon cable to the CD-ROM with only one connector. If that is the case and the burner did not come with a cable you have to buy a cable with two connectors. If you plan to leave the burner on the same channel as the CD-ROM get a cheap 40 wire cable. Dont get talked into the 80 wire cable as you dont need it and it is considered more reliable to use the old 40 wire cable on optical drives.
If by chance your CD-ROM cable has only one connector but the cable to your hard drive has two connectors you dont have to buy a cable. Set your CD-ROM drive to slave and make sure the hard drive is set to master rather than cable select. Plug the second connector into the CD-ROM and use the other cable to connect your new burner jumpered as master. That is considered the preferred way to set it up anyway.
Here are some instructions that explain it with pictures:
http://www.helpwithpcs.com/upgrading/installing_cd_recorder.htm