Hanoi's Noi Bai International Airport is about 35km north of the city and the journey takes from 45 minutes to an hour. The airport freeway is one of the most modern roads in Vietnam, although you'll see oxen herded by farmers dressed in rags crossing it. The freeway suddenly terminates in the suburbs north of Hanoi.
Vietnam Airlines minibuses between Hanoi and Noi Bai airport charge US$2 a seat. There are few information signs inside the new terminal building; you need to go outside and look for the signs for taxis and minibuses. Coming from the airport, the driver is supposed to drop you at the office of Vietnam Airlines at Pho Trang Thi, but the drivers usually tour the Old Quarter on the chase for commissions. If you end up dropped somewhere you don't want to be, just arrange a metered taxi to your destination: they are the easiest option if you have heavy bags, and there is no need to haggle.
The airport minibus service works reasonably well, but there are i few scams, especially at the airport. Normally, local touts (well dressed and posing as employees of Vietnam Airlines) board the official minibuses. They are skilled at befriending newly arrived passengers and by the time you reach the city will offer to recommend a 'good, cheap hotel'. If you want to avoid the sales pitch, just tell them that you've already got a hotel reservation, even if you don't.
To get to the airport from town, you can take one of the minibuses that depart roughly every half-hour from opposite the same Vietnam Airlines office on Pho Trang Thi. It's best - though not essential - to book the day before.
The cheapest way to get between Noi Bai airport and central Hanoi is to use public bus No 7, which runs all the way to the northern end of Hoan Kiem Lake, right on the edge of the Old Quarter. Services depart every 15 minutes from around 5am to 9pm and tickets are just 3000d - perhaps the cheapest airport run in the world. It can take more than an hour, however.
Airport Taxi (Tel: 873 3333) charges US$10 for a taxi ride door-to-door to or from Noi Bai airport. They do not require that you pay the toll tor the bridge you cross en route. Some other taxi drivers require that you pay the toll, so ask first.
Inside the terminal, touts will offer taxi services. Don't use the meter with a tout, as it may well be rigged. The 'official' taxi rank is outside the concourse and you buy tickets from the seller at the head of the taxi line.
In central Hanoi, there is always a collection of taxi drivers just outside the Vietnam Airlines office or at the northern end of Hoan Kiem Lake - it doesn't take much effort to find one. Don't pay more than US$10, including the toll.
There are also share cabs/private minibuses from travellers' cafes for about US$2 per person.