add a new column, or columns, to the cart object for this extra information.
In the add to cart button behavior, for the products that need this extra information added, set these columns to be up dateable from a text field.
This wil store the customer information in the cart along with the other item info.
in the order details table, you'll need to add columns for the extra columns added to the cart.
in the store order details behavior, you will need to bind the new cart columns to the new database columns.