Aston started playing rugby union at the age of eight in his home town of Castleford. He played one or two games but decided to switch to rugby league. He moved on to Stanley Rangers ARLFC, which is in Wakefield, then after a couple of years on to Oulton Raiders, where his father played as an amateur, until the age of fifteen. He moved to Castleford Lock Lane for one season, then started playing at under 17 level for Castleford. Despite an offer of a professional contract with his home town club, he decided to accept an offer from Sheffield Eagles. At that point he had been playing open age rugby for Selby Gaffers, coached by his father Brian, and had made his first Eagles appearance as an unnamed trialist on Easter Day 1985.
Winning the Man-of-the-Match in the 1998 Rugby League Challenge Cup final was the highlight of Aston's playing career. He controlled the game and drove the team to execute the game plan devised by Eagles' coach John Kear.