How can I update/add existing data from one set of tables to another?

Hello,

I have a old set of tables that I want to import into a new set of tables from. I've copied the old tables into the new db to make thing easier but the table structure is a little different for the new tables.

How can I copy the data from the old tables into the new ones?

So for example...

OLD TABLE REF
tbl_old_customers
tbl_old_orders


NEW TABLE REF
tbl_new_customers
tbl_new_orders


OLD TABLE CUSTOMERS: customer_id, customer_name, customer_address1, customer_city => NEW TABLE CUSTOMERS: cust_id, cust_name, cust_addr1

OLD TABLE ORDERS: customer_id, order_date, order_payment_type => NEW TABLE ORDERS: cust_id, ord_date, pay_type

Thanks for the help, I believe once somebody shows me how to do the customers table, I can figure out the orders table unless there's some sort of inner join process that can happen to do both.

Brian