You will have to have a mounting bracket secure to the frame of the PC case,
and mounting screws for the 3rd hard drive.
You will have to have a second ide port.
You may need an ide ribbon cable.
If its crowded, you may need additional ventilation.

If your two hard drives are on the same (primary) IDE cable and you have a CD or
other optical drive on the secondary IDE cable, you can put a third hard drive on
the secondary cable with the optical drive.  Jumper the third hard drive as Master
and the optical drive as Slave, unless the third drive is a Western Digital.  With a
W-D drive, you'd set it as Single and the optical drive as Slave..

If the optical drive is using a 40-wire, 40-pin cable, you may want to replace the
cable with a newer 80-wire, 40-pin cable.  If the drive is "faster" than ATA-66 and
the motherboard IDE controller supports greater than ATA-66, you'll need the newer
cable to utilize ATA-100.

Your pc likely has two IDE channels. Each IDE channel can support two
devices, for this scenario that means any combo of hard disks and/or cd
drives with the caveat that there must be one hard disk on the first IDE
channel and it's designated "master" (or first if using cable select
settings) for the OS. Note - BIOS settings can change this basic requirement
to use a second hard disk etc. to boot.

Normally one receives a pc with the hard disk set to "master" on the first
IDE channel and the cd drive set to "master" on the second IDE channel. That
means one can add two hard disks as "Slave" on the respective channels.

You having two hard disks and presumably a cd drive working now means you
must have two ide channels available which means you can temporarily add an
additional hard disk to make your backup. Hopefully power supply provides
enough leads (many don't) but one can get a splitter to provide two power
plugs from the one lead.