I've found out recently that any sort of basting or make-up brush works well for applying DE. You dust it around: on the inner/outer rims of your planting containers, in the carpets or on the floor, in crevices such as in and around the baseboards, windows and window sills, etc.
Matt is correct in that too much will lead to messy top soil, and hinder air exchange. You really don't want to cake it on, or get it wet; it is a pain in the ass in my experience, so I don't bother with it on my soil anymore but I'll try to put it anywhere else I can. The gnats will fly around and land on the floor and hide in crevices. If the area has a dusting of DE then odds are the adults will come in contact with it, and they should die within a day or two.
The gnats will lay eggs via whichever entry points they stumble upon, including the drainage holes if they have access so I would dust around there and the floors and try to get the adults on top of the soil with sticky traps, pyrethrum or another spray on insecticide and then the eggs and larvae with BTi and/or an insecticidal drench.
DE is primarily silicon dioxide (85%) with other elemental oxides (aluminum, iron, calcium, magnesium). It could potentially be used to raise soil pH if it was part of the mix, but I would agree with Matt in that the amounts used for your purposes would have next to no influence on in.
