Martha Jones was a medical student in London when she first met the Doctor as a patient in the hospital that she was interning at. After helping the Doctor get the hospital back to earth from the moon, the Doctor invited her to come with him a s a traveling companion in his TARDIS.

Martha Jones was instramental in defeating the Master after he had taken over the earth.  She was able to teleport off the Valiant using Captain Jack's watch as the Toclofane  invaded Earth at the Master's behest.  Martha spends the next year on Earth wandering from continent to continent spreading the Doctor's message to believe in him.   

After her time with The Doctor, Martha joined U.N.I.T.  U.N.I.T. pushed through her P.H.D. and Martha is now a full fledged Doctor.