Like so many other aspects of this lifelong process of learning to paint, previously I could not imagine focusing on something so mundane and technical, but I find it saves me so much time and headache later that it's worth the investment. And now I actually enjoy the sort of easy, meditative process of cleaning and preparing my surface.
First, I only paint on a dry surface that has had at least 20 hours to set for underpainting medium, and 40 hours to set for slower-drying painting medium. Painting on a gummy or tacky surface just makes a mess. (The recipes I use for painting medium and underpainting medium are in my Materials post)
Next, I use a tiny folded piece of 12oo grit sandpaper to lightly rub the surface of the completely dry layer from the previous painting session. This loosens any lint or grit that dried into the previous layer, which can then be lifted off by lightly dabbing with a small piece of masking tape.
The abrasion also gives the dry layer more "tooth" so the wet paint sticks - otherwise the oil tends to bead up.
(Abrading makes the surface a bit cloudy, and the previous rich oily areas look chalky and ugly. It's ok though, the luster comes back easily.)
Once I have a lint-free, abraded surface I use a soft filbert brush to apply a thin layer of painting medium - but only to the area I plan to work on in this session. Even a thin layer can sometimes drip or run, so I use a clean, microfiber cloth to wipe away most the oil.
This oiled surface is called a "couch" - I'm not sure why except that painting on it feels like sinking into a comfortable couch, the paint flows off the brush so easily.
To start painting, I pre-mix my puddles of values and colors on my palette with my palette knife, and then re-wash my clean brushes in Natural Turpenoid, to get rid of any dust that may have settled overnight, and also to re-wet the bristles. Then I dry the brush on a clean cloth and dip it into my painting medium.
After all that, I'm ready to start painting!