We first come across Steven Taylor two years after he has crash landed on the planet Mechanus. The Doctor, Ian , Barbara and Vicki meet him during The Chase as they are being pursued across time by the Daleks. It is only after Ian and Barbara have left the TARDIS at the end of the adventure, that the Doctor and Vicki return to the ship to find Steven has stowed away in order to escape the mechanoid city. Like many companions after him, the Doctor accepts this uninvited guest and the three of them are embroiled in a new adventure.
Steven can never be said to be the smartest of companions, but would capably handle any physical challenges. He was strong willed and certain of what was right and wrong, and above all else, believed in protecting human life.
That is why he is greatly troubled by the deaths of Katarina and Sara Kingdom and begins to question why the Doctor can't prevent such horrible events. Before he can decide to leave the Doctor, a new companion, Dodo, joins the crew, and Steven decides to stay on.
Eventually, Steven does decide to leave the TARDIS at the end of The Savages, when he decides to accept the responsibility of leading the combined society of Savages and Elders that is attempting a lasting peace.