When we first meet the Doctor in An Unearthly Child, Susan Foreman is his only traveling companion, and from all appearances has been traveling with him for quite some time. To further Susan's education, or maybe just to give her some social contact, the Doctor would occasionally stop the TARDIS and let Susan attend school where she could be around kids nearer to her own age.
Although Susan appeared to be a normal teen aged earth girl, her mental abilities and intellect were far beyond anything capable on this planet. It is pretty clear that Susan comes from the same planet as the Doctor, and indeed she calls him Grandfather. Whether they are truly related or not is never truly clarified.
Susan was frequently intelligent and capable in her adventures aboard the TARDIS, yet she could also be easily frightened and sometimes hysterical. Perhaps, much like earth teenagers, her mood swings can be explained by an abundance of hormones flowing through her body. Whatever might be the case, she was always devoted to her Grandfather and appeared to be very fond of him.
It was during their adventure in The Dalek Invasion of Earth, that Susan decided to leave the group . She had met a freedom fighter named David Campbell who was fighting the Daleks in the year 2164. The Doctor leaves in the TARDIS, thinking he is giving Susan a chance to have a happy life.
Although Susan returns for a brief appearance in The Five Doctors, we never learn much about what her life has been like since she left the TARDIS. However, more of her story can be found in recent Big Finish audio adventures.