Atar has an airport which used to be served by a daily flight from Marseille, France but as of writing there are only small charter flights available due to the kidnappings in other parts of Mauritania.
By train
The Iron Ore Train typically departs from Nouadhibou sometime between 2:30 pm and 10 pm, depending when the cargo is finished loading. There is only one train a day with passenger cars and tickets can be arranged in advance or bought at the Nouadhibou train station Gare Voyageurs for around 1500 ouiguiyas. Travel in the bucket cars is free, just climb aboard, but be forewarned it will be cold and dusty. The train stops at Choum where you can easily grab a ride to Atar in one of the many bush taxis or pickups which will meet the train for around 1500-2000 ouiguiyas.
By road
There is a paved and fast road which runs from Nouakchott to Atar served by a variety of minibuses including one run by a kindly French ex-pat and bush taxis. All of the rides going to Atar tend to leave [Nouakchott] from the Garage Atar at the end of town. Typical fare is around 4000 ouiguiyas.
Bush Taxis or 4x4's to Choum, Chinguetti, or Nouakchott can be arranged in the Garage, the market or at most hotels.