The hotel itself is located in Al Garhoud on Casablanca Road. It is about 2 minutes drive from the airport.
Emirates has free shuttle buses that run every 10-20 minutes from Terminal 3 arrivals. When you exit arrivals, turn left and follow the signs for "TAXI". Just before exiting the building to the taxi stand, you will see a red sign on the left that advertises "EMIRATES HOTEL TRANSPORT" (or something similar) as well as the complimentary bus service from Dubai to Al Ain/Abu Dhabi. Report to the staff member at that desk and they will ask you to take a seat till the next shuttle comes around, and then lead you to the correct shuttle.
It's a very simple process but be prepared to be treated as just a number being shuffled through the system!