Ty,
At the back of the PC, where all of the cables are, you will see largish screws. Undo them and one side of the computer will open (this all depends on make and model). Inside you will see 5 main things...the motherboard, which is the main circuit board, lots of ribbon cable and three drives. One of the drives may be made of plastic and is the floppy-drive (smallest of the lot) one is the CD-Rom (this is the thing that is attached to the cup-holder at the front of the computer[

)]).
Lastly there is your hard-drive. It is often silver and black and is about the same size as.....erm....er...a small book !!!
It will be held in place with a few screws. Undo them. Then
unattach the ribbon cable and a small power lead from it - hey presto.
Unplug the PC first!
When you open your new computer, you will almost certainly be able to swap the disks over and all that will happen is the operating system will automatically find new hardware and when done, it will look exactly like the one at home.
If you want to be really flash you could install removable disks in both PC's, then you can move your disk back and forth.
HTH
Glen