Oil paints dry by oxidization. That is, the paint adsorbs oxygen and polymerizes, forming long chains of molecules that are leathery and strong. They are real tough, you can find 19th century paintings in many antique shops and they aren't particularly valuable or scarce. Until modern times oil paintings were one of the toughest things man made. Linoleum is the name that was given to a floor covering product that was made by soaking sheets of cardboard in linseed oil. Today what we call linoleum is no longer made this way, but you will still occasionally happen onto a piece in old farmhouses in New England.
How fast your paintings dry is controllable to some extent. Here are a few of the things which influence that. The first would be your medium, if you use no solvent and lots of linseed oil your paintings will dry very slowly. If you use turpentine your paintings will dry more quickly. Many painters today, myself included, use alkyd mediums. The two best known are Liquin and Galkyd. Both of these products give a faster drying time. I wrote more about these here. Alkyd mediums speed drying a lot.
Another way of getting alkyd into your paintings but continuing to use the medium that you are using now, is to switch an alkyd white. Winsor Newtons Griffin line is a good one to try, you can use it mixed 50/50 with a regular titanium white if you prefer. This is a sort of set and forget solution, that is all you have to do is use that white and the painting will dry quickly, as white is in most of your mixtures, particularly those which are thick and would dry slowly.
There are dryers that are made to be added to paint. The two most common ones are Japan dryer and cobalt dryer. Japan dryer is a catchall name for a number of different concoctions the most common of which contains napthenic acid. These days with the prevalence of alkyds painters don't seem to use dryers as much as they did years ago. Nowadays Japan dryer seems to be more of a craft supply or used in the building trades rather than over here on the fine art side of the wall. I think that is a good thing.
I remember R.H. Ives Gammell holding up a little bottle of cobalt dryer at us and warning "gentlemen there is enough dryer in this little bottle to crack every painting you will make in your lifetime" His advice was not to use the stuff and with a couple of exceptions I have followed that advice. Cobalt litholeate dryer is poisonous and is commonly added in small amounts to mediums or into the white on the palette. I do recommend against its use. The problem with dryers is this........
They may continue to dry the paint film more than is desirable until it is dessicated, shrunken or embrittled. Oil paint is so tough because it remains gummy rather than drying out completely. I was taught long ago to say when asked how long it would take for a painting to dry the answer was "dry to the touch in three days, dry all the way through in four hundred years. I tell clients this and the other things on this page, because it is important for them to be reassured that their expensive painting is going to last a long time. I have asked people what the picture on their new flat screen television is going to look like in three hundred years.
Different pigments have different drying times and that will effect how rapidly your paintings dry tomorrow I will discuss that.