When you get the new computer try to put it in as a slave as mentioned before.
Its quite easy, you need to move a jumper on the back of the hard drive to put it in slave mode, how to move it is displayed in the drive.
If its the old style with the wide connector, just put it to the ide connection on the new motherboard using the old cable but change the connection to the one in the middle for the HD.
If its an sata just plug it in.

Then connect the power to the hd and start the computer, if everything is right it should appear under the rest of the drives in the tree under something like e: or whatever is avaiable on that computer.