To apply oil, I use a boar bristle shaving brush, onto which I put a few drops of oil. Generally Clenzoil or Ballistol for blued firearms. It puts enough oil on the weapon without putting too much, and evenly distributes the oil into the nooks and crannies.

Then a quick wipe with a clean rag.

To clean the brush every now and then just swish it around ina can of Mineral Spirits.

I picked this up from my Father who was Brown Shoe Army.