The easiest way is to use usb datalink cable if your old one has usb port. £11.74 from ebuyer click here. (you can find cheaper usb1 version, do not remember the link). Software come with cable, very easy to use.
If you old one does not have usb port, you can link two PC via parallel (print port). Cable can be found from ebuyer around £5, you can search yourself. Software, windows from Win95 have a function called direct cable link. You can set it up. Search help on windows to find how.
Another way that I have used is to open the box of your new machine and take the HD from your old computer and fit it into the new as a slave drive then just copy the data accross to your new hard disc. When I say fit it into your new computer I dont mean that you need to go to all of the trouble of screwing it down, just connect the wide ribbon cale after setting the jumpers on the drive to slave. Then connect up the power lead to the drive and you should be ready to go.