Grit your teeth to keep out the big stuff. Seriously, treat a sandstorm like a blizzard and stay put. With your world reduced to a few feet around you, you don’t want keep walking and risk falling off a ledge, wandering off course, or getting lost. The majority of sandstorms are short-lived so holing up for a while is the best solution if the storm is upon you.
Think like a cowboy, and hunker down next to a boulder, under a ledge/cave, or other semi-protected area; cover your mouth and nose with a bandanna, spare shirt, or just pull your shirt up to protect your respiratory tract. Sunglasses and gloves along with long-sleeved shirts/pants and a brimmed hat are must-have items for desert travelers and can all help reduce exposure to the sandpaper—the action of the wind during a sandstorm.
I was once caught in a sandstorm while teaching a desert survival course for the military in Arizona. Before the storm overtook us, we picked up our pace and made it to a huge boulder-field in the open desert. Once the storm hit, you could hardly tell there were boulders near us and the person on my left and right were partially obscured. We sat down, covered up our heads with large scarves, and rode out the brown blizzard while the temperature plummeted thirty degrees or more. Two hours later, the storm dissipated, the sun was out again and we were baking in the heat.
If you are driving on the highway when a sandstorm hits, exit if you can. Otherwise, pull off the road a safe distance away from other vehicles, turn off the engine (or you will get all that fine debris in your air filter), and wait it out for the next hour or so.