Catalysts are equipped as weapons and can be used on either the right or left weapon slots. Pressing R1 or L1 (depending on which side the catalyst is equipped) will cast the selected spell. R2 produces a fast, but weak attack, while L2 is a standard parry.
Below is a list of all the Catalysts in Demon's Souls. Clicking on any of the names of the Catalysts will give detailed information about that item on a separate page.