The battery in your Cavalier is removed just like the battery in your other car; the terminals are just shaped somewhat differently.
If you look at the battery cables, you will see that they are attached to the side of the battery with bolts; simply unscreq the bolts holding the cables to the battery and they will come right off.
There is also a plastic clamp holding the battery to the tray it sits in; look down along the side of the battery and you will find the clamp; use a 13mm socket to loosen the blot holding the clamp down and you will be able to lift the battery right out.
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