Well, you could either serialize the array, or just create two tables, one that contains general order info and assigns an orderID to the transaction (unique auto_increment field, for example). Then, in a separate table, you'd insert one row per item in their cart, each row having an "orderID" column that would tie all of them to the row you inserted in the first table.
Then, when it came time to process the order, it'd be a simple JOIN in SQL to retrieve all rows from the table containing individual items that match the given orderID.