There are two mobile operators: Dhiraagu and Ooredoo. Both of them sell local prepaid SIM card with internet connection at competitive rates. The first mentioned of them is the leading local telecom company which has wider coverage while prices are about the same with its competitor. They both have shops right next to the airport arrivals area upon exiting. Also both offer 3G/4G data connections. Also if you plan to sail maybe you can be interested in satellite service offered by Ooredoo.
Most hotels and cafés offer public Wi-Fi but as of 2016 connections are usually really slow, between 56-500 kbps. A local mobile number is needed to purchase time at many Wi-Fi spots around the country.