There is no public transportation system in this town, so I would recommend car rental if you can, because the cost of a taxi cab is astronomical.
The closest the city comes to public transport is the use of a trolley system, but it can only be used by patrons of certain hotels in a certain area.
Arlington is just 15 minutes form Dallas/Fort Worth International Airport. Take the south airport exit to 360 south.
You can get around Arlington's famous 3-square-mile entertainment district by taking the Trolley shuttle which makes stops at Six Flags Over Texas, Hurricane Harbor, The Ballpark and some hotels in the entertainment district.