If you have no experience with this, it might be easier to just copy the data from your Dimension to a external usb harddisk and then to the XPS. But i will try to explain it.
I've looked a bit around: your XPS hard drive is a SATA drive, while your the drive in your Dimension is probably a PATA-drive (just connection types. Look at the hard drives and compare them with this image
to see which types they are.)
As far as I know the XPS 530 has a Foxconn G33M-S motherboard, which contains one ATA (PATA) connector. So you should be able to just connect the hard drive from your Dimension into the XPS.
To make it work properly, you should set the drive from the Dimension to slave. This can be done by setting the jumpers next to the cable connector. The jumper setting depends on your hard drive model. Usually the possible settings are shown on the hard drive.
If you feel uncomfortable with this whole thing, you could ask someone, who has some experience and who you trust to do it for you, or just use an external usb hard disk
Make sure the computers are off and disconnected from the power outlet, when you open the case...
Dell offers a user manual for your Dimension and XPS. Maybe it's of some help by removing and placing the various parts...
Please tell me how it worked out.
As you probably understand, I can't take any responsibiity for damage to your system...
If you have any problems, just post them here!