From Noi Bai airport to Hanoi Old Quarter, there are taxis that run at fixed rates waiting outside of the arrival hall. It costs between 345,000 - 375,000 VND depending on the type of taxi you get (or $16-18). Three official taxi brands for airport routes are: Noi Bai Taxi, Viet Thanh Taxi and Dai Nam Taxi, you can also take a request to us to book a private taxi here http://www.mrlinhadventure.com/en/contacts-us.aspx
In any case, do not go by the meter because the rate will be much higher than the fixed rate. You also need not pay any toll fees. Tips are not required though if the driver is really nice you can also give tips.