Baird was born in Rotherham, West Riding of Yorkshire, England.
Baird was born a Yorkshireman but started his career at Southampton in 1982–83. He never really managed to get that many appearances under his belt. He spent part of the 1983–84 season on loan at Cardiff City having a fairly successful loan spell scoring 6 goals in 12 matches. At the start of the 1984–85 season he moved on loan to Newcastle United, but here he only made 5 appearances and scored only 1 goal.
In March 1985 after only 22 appearances and five goals for Southampton he moved to Leeds for £50,000. Despite not scoring many goals, Baird's first spell at Leeds was a success. His aggression, whole-hearted attitude, skill and goals made him immensely popular amongst the Leeds fans. Baird was made Leeds captain by manager Billy Bremner at the start of the 1986–87 season and his performances alerted Portsmouth to his abilities, as he helped lead Leeds to both the FA Cup semi-final (lost 2–3 (aet) to Coventry City and the final of the inaugural Second Division promotion/First Division relegation play-offs. Leeds drew the two-legged play-offs final with Charlton Athletic (1–0, 0–1) but lost a one-off deciding rubber (1–2 aet) at St Andrews and remained in the Second Division.
At the end of the season with Portsmouth having just been promoted, he moved to Portsmouth to help them in their quest to keep their division one status. He was sold for £285,000 having played 101 games and scored 37 goals for Leeds., but failed at a higher level, scoring only one goal in his 20 appearances for the club in the 1987–88 season.
Portsmouth were however struggling financially and in March 1988, Baird was sold back to Leeds for a snip of the price they bought him for (£120,000). Baird was once again successful at Leeds picking up player of the year in 1989 but with the arrival of Lee Chapman to help with the promotion push in 1989–90 Baird was deemed surplus to requirements by Howard Wilkinson, having played 91 games and scored 21 goals
In January 1990 he was sold to Middlesbrough for £500,000. Baird's involvement in the championship didn't stop there. On the last day of the season Baird scored two goals against Newcastle United, and this along with Leeds' victory over Bournemouth clinched promotion for Leeds over Newcastle in third place (Leeds winning the title on goal difference over Sheffield United). With Leeds winning the title Baird picked up a winners medal, even though he was not at Leeds any more due to him having played enough games for the club in the season.
Baird stayed at Boro until the end of 1990–91 when he moved to Hearts. He later returned to England, playing for Bristol City, Plymouth Argyle and Brighton & Hove Albion before retiring in June 1998.
After retiring from his playing career Ian went to Hong Kong taking charge of Instant-Dict, a team in their top division, and also the national side in 1999 for the 2000 Asian Cup qualifiers. He also played non-league football for Salisbury City (1997–2000) and Farnborough Town (2000–2001).
After returning from Hong Kong he worked for a Leeds-based football agent but resigned after 3 years as he didn't enjoy the job. Ian set up his own contract hire and vehicle leasing company in 2003.
He took over the part-time managerial post at Havant & Waterlooville in November 2004. He currently lives in Southampton with his second wife and two teenage children.
On 3 October 2007 he was appointed manager at Conference South rivals Eastleigh, taking over from David Hughes. After five years in charge, he was dismissed on 11 September 2012.
Baird was appointed head coach at Sutton United in October 2014.
Baird's authorised biography, Bairdy's Gonna Get Ya!: The Ian Baird Story, written by Marc Bracha, was published in September 2013.