I'm posting this info here to help others because I couldn't find anything clear and useful on the internet.
There is a still cheaper way. Abu Dhabi municipality runs frequent buses between the airport and the main bus stand (a.k.a the taxi stand). One can take bus number 901 on this route. Buses are available round the clock at 30 mins interval during the day and at a 45 minutes interval during the night.
For trips starting from the bus stand, the bus stops at the second row inside the bus stand. You will find a yellow signboard that has "901" and the arabic word "Mataar" (meaning airport). That's where you get the blue-and-white bus to the airport. Tickets cost AED 3.00 and can be purchased inside the bus.
At the airport, step out through one of the doors and walk all the way forward in the direction of traffic, till you reach the end of the building. Keep walking till you see a blue signboard that says "Abu Dhabi Municipality Bus stop". Wait there for the bus. The buses are blue and white in colour and costs AED 3.00.
Abu Dhabi City Terminal:
If you have heavy luggage and you want to ride the bus, there is an alternative. You can check in at the City Terminal which is inside the city (beside Beach Rotana Hotel, diagonally opposite the Abu Dhabi mall). This is like an extension to the checkin at the airport and you can check-in, obtain your boarding pass and dump your checked-in luggage. Then you can proceed to the main bus stand and take the bus to the airport and travel light with just your cabin baggage. The City Terminal does NOT provide a complimentary transfer by bus to the airport as advertised on some websites.
1. If you're planning to use the bus, make sure you have ample time before your flight starts boarding. You may not get a bus right away when you arrive at the bus station.
2. There are two terminals at Abu Dhabi airport. Make sure you know which terminal your flight is on, and tell the bus driver which terminal you want to go to. Drivers tend to "assume" everyone is going to Terminal 2. :-)