I've read many first hand accounts and it goes something like this...
The desert lies looking perfectly ordinary as the countdown reaches zero. Instantly there is an intense light which dazzles you even through your welding goggles. The light is many times brighter than sunlight and seems almost thick, almost like a liquid. Soldiers lying 3 miles from an atomic blast, crouching in slit trenches, facing away from the blast with their eyes closed and covered with their hands could clearly see the bones in their hands right through their closed eyelids. It's that bright. And the heat! Along with the light comes a sudden flash of heat so intense it feels like it will burn right through you. Any closer and it would be hot enough to ignite your clothing in an instant.
After several seconds this light slowly starts to fade, allowing you to recover some of your eyesight. Before you, rising majestically into the air, is a roiling, boiling mushroom cloud. The column from the ground is glowing orange like a billowing fire, rising and disappearing into the rolling mushroom head. The head is glowing a hideous purple color. The size of the cloud makes the desert look like a very small place, even though it is quite large. The impression is overwhelming and leaves you stunned and speechless. This is much, much bigger and awesome than you had pictured. It's almost too much to handle.
After about 30 seconds the blast hits you. It's not like a strong wind, it's more like someone trying to body-slam you. Some of your colleagues crumple under the blow. They're not hurt, just overcome for a moment. Immediately afterward a *second* blast, almost as strong, hits you from behind. Dust has filled the air, making it hard to see. Despite this, above the mushroom cloud still grows taller. A thunder-like roar arrives with the blast wave, continuing for nearly a minute. It only slowly fades away.
Finally the dust has settled. The mushroom cloud still hangs above, but it has stopped growing and the upper parts are starting to drift to one side with the wind. You can see it is starting to dissipate.
This description is for a medium sized warhead being set off about five or six miles away. There would have been buildings, towers, tanks and such set up at different distances from the blast to study effects. No researchers would be near these until afterwards. Observers would be confined to a supervised area a safe distance from the blast.