Born in Sochi, Russia, Lediakhov started playing professionally with modest FC SKA Rostov-on-Don. In 1990, he joined FC Dnipro Dnipropetrovsk. After impressing with FC Rotor Volgograd, Lediakhov was bought by Soviet Union giants FC Spartak Moscow, being essential as the capital team conquered three consecutive league titles, which included the inaugural edition of the competition, as the player scored in double digits in two of the three seasons. In the 1994 summer, 26-year-old Lediakhov moved abroad, signing with Spain's Sporting de Gijón. Even though he netted nearly 50 overall goals for the club whilst showcasing good offensive skills, his eight-year-old stay in Asturias was an inconsistent one, marred by irregular performances and disciplinary problems: he received a six-match ban after a 22 February 2000 match at Albacete Balompié, after assaulting an opponent then repeatedly pushing referee Téllez Sánchez after receiving his marching orders. At the club, he teamed up with compatriots Dmitri Cheryshev, Yuri Nikiforov and Alexei Kosolapov. Lediakhov also spent a few months in Japan, after which he returned – with the club now in the second level – having further disciplinary problems which led to a suspension. He eventually bought out his contract and retired in 2003 at the age of 35, after one season with SD Eibar also in division two.
In 2007, Lediakhov worked as sporting director at FC Rostov. On 6 June of the following year, he was assigned coaching duties at Spartak Moscow's youth teams. From August to September 2008, Lediakhov served as caretaker manager of the club, later working as assistant under both Michael Laudrup and the Dane's successor, Valery Karpin. On 22 December 2009, he was appointed head coach of FC Shinnik Yaroslavl, staying in charge for approximately five months. On 9 May 2011, he was announced as new director of football at FC Rotor Volgograd, for which he also acted as scout. Lediakhov returned for a second spell as Spartak's assistant, on 6 September 2011. On 7 April 2018, he became the caretaker manager for Russian Premier League's FC Akhmat Grozny following the resignation of Mikhail Galaktionov. On 22 May 2018, he was signed as Akhmat's manager on a permanent basis. He resigned from Akhmat on 2 September 2018. On 20 September 2018, he signed with FC Baltika Kaliningrad until the end of the 2018–19 season. He was dismissed by Baltika on 19 December 2018.
