Richardson was born in
Newcastle upon Tyne
 where he played football for Montagu and North Fenham Boys club.
 He joined
Everton as a schoolboy in 1978 and turned professional in 1980. A versatile
midfielder, the young Richardson often had to be content with deputising for the likes of
Peter Reid and
. However, he still carved out a semi-regular place, and played in the Everton teams that lost the
Liverpool after a replay
 and won the
FA Cup in 1984. He won a
together with that of
UEFA Cup Winners Cup winner's medals the following year. He made 113 appearances in all for the Toffees, scoring 16 goals.
He moved at the start of the
Watford, but only spent a season there before moving on to
Arsenal for £200,000.
 Richardson succeeded
Graham Rix on the Arsenal left wing, and played in the
as Arsenal lost to
 before moving over to the right for Arsenal's
title-winning season to cover for the injured
. Most notably, Richardson played in
Arsenal's dramatic victory at
Anfield where they won the title in the last minute of the last game of the season. Now a Championship winner at two different clubs, Richardson continued to be a regular the following season at Arsenal; however, he never totally got on with Gunners manager
 and he was transferred to
Real Sociedad for £750,000 in the summer of 1990. He made a total of 121 appearances in all competitions for Arsenal, and scored eight goals.
Richardson's time at Real was short. He moved back to England in the summer of 1991, signing for
Aston Villa for £450,000, and was an ever-present in his first two seasons at the club.
 Richardson became Villa's captain, and led the club to runners-up spot in the
inaugural season of the
Premier League and victory over
Manchester United in the
 in which he won the Man of the Match award.
 While at Villa, he also won his one and only cap for
England, in a 5–0 friendly victory over
on 17 May 1994.
Richardson followed his old boss Atkinson to
Coventry City in 1995, and spent the next two-and-a-half years at the Sky Blues repeatedly fending off relegation under both Atkinson and his successor,
 He left Coventry in September 1997, having scored once in the League Cup against
 and had spells at
 and finally
 Richardson retired from playing in 2000, his career finishing on a low after Blackpool were relegated to
in his final game.