Your computer appears to use SATA to interface between the motherboard and the DVD drive. You will need to purchase a new SATA capable 5.25" DVD drive in addition to a SATA cable to connect the DVD drive to the SATA header on your motherboard. Depending on how your BIOS is configured you will need to press the key that flashes on the screen during startup to enter the setup and enable the SATA port. Then install the drivers in Windows.
[http://downloads.dell.com/Manuals/all-products/esuprt_desktop/esuprt_inspiron_desktop/inspiron-580_service%20manual_en-us.pdf|Dell Inspiron 580 Service Manual]