From Wikipedia

The series takes place fifteen years after the film's story and features the return of the alien as a clone of deceased photojournalist Paul Forrester to spend time with his now teenage son Scott Hayden, Jr. as they try to avoid a U.S. government agent and find the missing Jenny Hayden.
 
Each episode of the series had the fugitive father and son moving from place to place meeting people that were in need of some assistance, while Scott tries to explain to his alien father what it means to be a human being and Starman must deal with fallout from Forrester's rather hedonistic past.
 
http://en.wikipedia.org/wiki/Starman_(TV_series)