...How do I connect the drive to a different PC?
You have to physically remove it from this PC. As you've said it's an older system, it's most likely an IDE hard drive (has a wide Data cable with 40 connectors and a 4 pin power connector), rather than the newer SATA drives (narrow Data cable with 2 connectors - may be integrated with a 7 pin power connector), which means it has a Jumper to determine if the drive is a Master or a Slave. The settings are usually marked on the drive label. There is also a Cable Select position.
I'm also assuming it's a desktop, not a laptop.
To connect it to another PC you just have to connect the Power and Data cable (with Power Off of course) to the other PC (doesn't have to be physically installed, just make sure nothing is touching the circuit board on the hard drive, and the hard drive case doesn't touch anything on the other PC but the case). How to set the jumper depends on just where you connect it, and if the other PC's drives are set to Cable Select, or Master/Slave. If Cable Select, just jumper this drive for Cable Select and connect it.
Older PCs have two IDE ports on the Motherboard (Primary IDE and Secondary IDE), each can have 2 devices connected. A typical setup would be a hard drive on the Primary controller as Master, and a CD/DVD drive on the Secondary controller as a Master. So this drive could be connected to either IDE controller, but would have to have the jumper set to the Slave position. If you don't need the CD/DVD drive to burn your data to disc, you could disconnect the CD/DVD drive and connect this drive without needing to change the jumper.
Newer systems that use SATA drives may only have one IDE port -- it may be unused if it has a SATA CD/DVD drive. If so, you could probably connect this drive without changing the jumper. It's possible the Boot Sequence in the BIOS is set to IDE first, which would have been ignored since nothing was connected. So if it tries to boot to this drive, the boot sequence in the BIOS needs to be changed.
Another option would be to purchase an external USB enclosure, then put this drive into the enclosure. Then you just plug it into the USB port on the other PC. Just be sure the size matches (Laptop usually 2.5", Desktop 3.5") and the Internal Interface is correct (IDE or PATA, not SATA)
A Live CD is an easy option to copy the data to another PC over a network connection, or burn it to CD, without having to open up the PC, but for the
Ultimate Boot CD for Windows you need access to a WinXP CD, and the Linux versions may have a steeper learning curve than physically moving the drive will, depending on how mechanically inclined you are.
HTH
Jerry