Once you have a cart, on the inventory screen(F6 button), click to the part that you want to move to your cart(Weapons/Armor, Magic Items, misc items(?), ingredients) Click wagon so the wagon picture appears on the right column, click remove, then click on the items you want to move to your wagon. You know it's moved there when the number appears with the wagon picture changes(denoting the weight of the items you moved to the wagon)... to get them back into your inventory, it's a similar process... select wagon, select remove/equip, use the arrow keys on the rightmost to scroll through your wagon items, then select the items you want to move back...
One more thing... you can't put money into your wagon(unless they're still a pile rather than on your GOLD button, but that's a bug)... they're stored in banks or converted into letters of credit instead(also with banks)