There are special applicators like the 'Easy Squeeze Duster' available. To me the prices seem too high. And yes please always wear a dust mask and eye protection when you apply the dust, just as you would when applying anything else that might blow, drift, or spatter into your faces, nose and eyes.
If you don't want to mess with dust, I have read that you can mix the DE with water and apply in a wet sprayer. Once the water evaporates, the DE will begin to work.
DE available online seems to cost 3 times as much as the farm/feedgarden/tractor stores. I bought 1 1/2 pounds of the fine flour type for $4 the other day locally.