Salisbury was born in Northampton, England, and made his first-class debut for Sussex in 1989, taking the wicket of Ian Austin in both innings. The following year he claimed 42 wickets, albeit at a somewhat expensive average of 49.40, but his potential was recognised with a spot on the England A tour to Pakistan and Sri Lanka, and the following winter (again with England A) he toured West Indies with some success, taking 14 wickets at 27.42.

1992 was Salisbury's breakthrough year, seeing him pick up 87 first-class wickets at under 29 apiece, including six five-wicket hauls. He was rewarded both with being named one of the Wisden Cricketers of the Year in the next year's Almanack, and with his Test match debut.

His first appearance for England was in June 1992, against Pakistan at Lord's, and he did not rise to the occasion well enough, though in the third Test he made an important half-century in the first-innings. He was then dropped for the rest of the summer.

This was to become a familiar pattern, as England regularly turned to Salisbury now that leg-spin was being made fashionable again by the emergence of Shane Warne, and just as regularly discarded him after a couple of matches; never in his fifteen Test career did he play more than three games in a row. He was not good enough to prosper at the highest level, with a career Test bowling average of 76.95, and he has been rated as the worst specialist bowler in Test cricket.^[3] He played his last Test in 2000/01 in Karachi, with a series aggregate of 1–193.

In county cricket, however, Salisbury was a different man. He passed 50 wickets most seasons, and when he left Sussex for Surrey in 1997 he revelled in wickets that suited his bowling style. In successive seasons his bowling average improved: 31.20, 22.89, 22.19, and in 2000 he took 52 wickets at just 18.92, including a career-best 8–60 (and 11–101 in the match) at The Oval against Somerset.

1999 saw the first of Salisbury's three first-class hundreds, exactly 100 not out against Somerset as he shared a ninth-wicket partnership of 122 with Martin Bicknell. His second century (101 not out) came in 2003 against Leicestershire, and his third century (103 not out) came against Hampshire in 2007 sharing in a stand of 177 with Azhar Mahmood.

After 2003, Salisbury played increasingly less first-class cricket, and in 2004 he took just 14 wickets at an average of over 50. By 2005, he was making more appearances for the second eleven than for the first team. In 2006, Salisbury enjoyed the lower standard of cricket to be found in the County Championship's second division, and formed a decent spin partnership with Nayan Doshi, that played an important role in Surrey's promotion campaign.

Salisbury was released by Surrey at the end of the 2007 campaign, ending a ten-year stint at the club. This was connected to Surrey's re-signing of Saqlain Mushtaq from Sussex in the same month.

In November 2007, Salisbury signed a two-year contract with Warwickshire – following the county's failed attempt to lure Mushtaq Ahmed in the summer.

In March 2009, at the age of 39, Salisbury announced his retirement from first-class cricket. Salisbury initially accepted a two-year extension to his playing contract with Warwickshire, but instead decided to end his playing career, and take up a role as a coach with his former county, Surrey. He replaced the South Africa-bound Nadeem Shahid as the second team coach, being promoted to first team coach for the 2012 season.

On 17 June 2013 it was announced by Surrey County Cricket Club that Salisbury had been sacked, along with the first team director of cricket Chris Adams.

In May 2017 Salisbury was named as Head Coach for the England Physical Disability Cricket team.