On using Medium in Oil Painting
• Increase Transparency
• Alter the Viscosity
• Alter the Drying Time
I'll talk about these in a moment, but first of all remember:
• You don't have to use medium at all. If you do, be thoughtful about it.
• Observe the Fat over Lean rule:
Fat over lean means to use less medium at the start (ideally none, just thinning with solvent if needed) and use more medium (if desired) as you work on top to the finish. The issue is with varying drying times and potential cracking over the long-term if done the wrong way around.
Think of medium/linseed oil as fat, and straight paint [with or without solvent] as lean.
I am going to try and restrict my comments here mostly to mediums I have personally worked with. There is a lot out there.
If you want to get into laying a transparent "veil" of color over an area of dried paint, you will probably want to add something to your paint. The opacity of paint varies by the pigment, but for glazing, an additive is usually needed.
Most kinds of medium will accomplish this. Linseed oil will do the job. An alkyd-based medium like Liquin or Galkyd will do so while also speeding up the drying time.
Altering Viscosity (Thinning or Thickening)
Thinning the paint for increased "flow" is a common reason to add medium. Rendering certain kinds of things works better when the paint flows more. Linseed oil will do this, as will some of the variants of products like Liquin or Galkyd.
Oil paint is pretty good at holding marks when you want to paint in an impasto manner. ("Impasto" just means a thick paint application.) But sometimes painters want even more body and for that purpose there are so-called impasto mediums. Rublev/Natural Pigments makes one, though I haven't tried it yet. Winsor and Newton makes a version of Liquin called "Liquin Impasto Medium" which I have not used myself.
Altering the Drying Time
Depending on the color/pigment, oil paint can take days, or even up to a week to dry. That can be frustrating. Alkyd-based mediums like Liquin or Galkyd will generally halve the time most colors require to dry. Other factors affect drying time too, like light exposure and air circulation. A painting in a sunny room with good air circulation will dry faster than one in a dark, unventilated space.