Its really easy to make a reservation for room in dubai. Most of the hotels in dubai have their own websites , it would just take a little time to browse through the hotel’s site and book you room according to your itinerary.
Hotel reservation in dubai can also be made through any of the trusted travel companies like SOTC and Cox & kings. Travel agencies usually book hotel rooms in bulk and therefore get special rates. Most of the time room rates are cheaper when you go through an agent than approach the hotel directly.
One could approach the travel agency personally or through their site. You could also get your self a room through the agent at the airport but the rates may be a bit higher and its always advisable to have your itinerary sorted out before itself.