FROM-AND-TO NOI BAI AIRPORT
Taxi
On the way out of the airport, you will see taxi signposts. Follow these signposts, you will reach a parking area outside the airport where many taxis are waiting. There are some recommended taxi brands at the airport: Hanoi Taxi, Taxi CP, Taxi Airport and Mai Linh Taxi. It normally costs VND 300,000-350,000 (13.5-16 USD) and takes about 35-40 minutes with normal traffic to travel from the airport to Hanoi centre.
Door-to-door pickup
Another option is door-to-door service that can pick up you from the airport to your accommodation. Please check out these companies to find more information about door-to-door pickup service.
https://www.airportshuttles.com/hanoi.php
AROUND HANOI CITY
Taxi seems to be the most suitable means to travel around the city. Some trusted brands are: Mai Linh, Taxi Group, Taxi ABC, Taxi Sao Ha Noi. Please note that most people in Hanoi speak little English, so you might need to ask receptionists in your hotels for assistance.