Instructions
Purchase or locate "slotted" equipment, equipment that can accept expansion from slot items, like cards. Cards are much rarer and extremely expensive at shops, but can be obtained more easily by questing with high Luck companions.
Use an Identify scroll or spell to identify the equipment so you can modify it. This is usually necessary since you are most likely to obtain slotted equipment from killing monsters, which usually drop unidentified gear.
Place the equipment in your inventory, but do not equip it. Double-click on the card you want to use to compound with your slotted equipment, then click "Compund." A menu will appear with the options for slotted equipment to compound. Highlight the slotted equipment and click "OK" to compound cards.