Shared taxis go frequently from Atar for 300 old UM (which should equal 30 new UM, so don't fall for any price higher than that) per person. To get there with your own vehicle, you should leave Atar at the only roundabout in town bounding towards Bab Sahara and follow the road.
The town is small so it's easily to see it by foot. If you want to explore the nearby hills and the ancient paintings, it would be smart to wear proper shoes.
About 2 km from the town you can find ancient painting on the rock. The site can be reached only by foot.
Chances that you'll be invited for a tea by locals are great. They may even offer you a meal and a bed.
The best option is to sleep in Atar as it has a plenty of nice choices. Otherwise there is a nice Auberge in the town, though it's not known if it's still running. Friendly locals may offer you to sleep in their house too.
Atar seems to be the only option to go to next.