Oil keeps the hair soft and pliable by replenishing the moisture in the hair shaft.  The oil used needs to be able to penetrate the hair, so it should be a small molecule oil.  Jojoba oil is one of the finest oils and works well on fine hair.  Olive and coconut oils are slightly larger/heavier oils and work well on many people's hair.

These oils can be used as a heavy conditioning by using enough to make the hair oily and leaving on for 5 - 30 minutes.  Light conditioning can be done daily with some hair types.  This can be done with just a few drops of oil applied to the length of the hair - avoiding the scalp.  Oiling before bed allows the hair to fully absorb the oil by morning.  (I usually oil then braid my hair before bed.  This limits the oil from messing the bedding.)

There are many other posts discussing types of oils and techniques used.