Atar is a small town in Mauritania. There are four asphalt roads leading out of it.
Another goes west to Azougui - getting a lift here is easy, just stand by the size of the road just out of town (past the oued away from the central roundabout in the city) and hold your hand out with palm facing the road. Payment is usually not expected
Another goes west to Chinguetti and Ouadâne. Hitching is harder on these roads as the towns are quite touristy and not densely inhabited, and it's more likely that you'll have to pay for a bush taxi. However as with anywhere in Mauritania it's possible that you'll be offered space on the back of a passing pick-up truck for nothing.
The fourth goes south to Nouakchott and to Aïn Ehel Taya, where there is an army checkpoint at the turn-off for Terjît and Ouadâne. The military here are initially official but become friendly after you've chatted with them for a bit and can get passers-by to pick you up. It's possible to get a lift to Nouakchott but more likely that you'll end up taking a bush taxi.