Answer by taking a quote from the following article:

Anil Kumble ( pronunciation  born 17 October 1970) is an Indian former cricketer and a former captain of Tests and ODIs, who played Tests and ODIs for 18 years. A right-arm leg spin (leg break googly) bowler, he took 619 wickets in Test cricket and remains the third-highest wicket taker of all time (as of 2018, behind Muttiah Muralitharan and Shane Warne). Unlike his contemporaries, Kumble was not a big turner of the ball, but relied primarily on pace, bounce, and accuracy.

Kumble made his first-class debut for Karnataka against Hyderabad on 30 November 1989, taking 4 wickets and bagging a pair. He was then selected for India Under-19s against Pakistan Under-19s, scoring 113 in the first test and 76 in the second. He made his ODI debut against Sri Lanka at Sharjah in the Austral-Asia Cup on 25 April 1990. He played one more game in the series against Pakistan and ended up picking two wickets. His Test debut came in the same year when India toured England for a three-test series. It was the second test of the series played at Manchester and he picked up 3 wickets conceding 105 runs in the first innings and went wicket-less in the second innings of the match which resulted in a draw. He did not play any Tests until 1992. Kumble picked up 13/138 in Irani Trophy against Delhi for Rest of India which ensured the latter's victory. This performance helped him earn a place in the Indian side that toured South Africa and Zimbabwe. It was during the 1992 Indian tour of South Africa that he established himself as a quality spinner, taking eight wickets in the second Test. All in all he took 18 wickets at an average of 25.94 and with an economy rate of 1.84 in the four test series. Later that year, when England toured India, Kumble took 21 wickets in three Tests at an average of 19.8. He picked up seven wickets for 165 runs in the third Test of the series played at Bombay as India went on to win the match by an innings and 15 runs. He was adjudged man of the match for his performance.  Kumble took his first 50 Test wickets in 10 matches; the record remained the fastest by an Indian bowler till Ravichandran Ashwin surpassed him achieving the feat in nine matches. His 100 Test wickets in 21 Test matches, the second fastest by an Indian bowler after Erapalli Prasanna (who took 100 wickets in 20 matches). On 27 November 1993, he took six wickets for 12 runs in an ODI against the West Indies at Eden Gardens, Calcutta in the final of the Hero Cup, which was an Indian record for very long time. This record was broken by Stuart Binny on 17 June 2014 against Bangladesh. In January 1994, when Sri Lanka toured India, Kumble picked up his first 10 wicket haul in his 14th match which ensured India's victory by an innings and 119 runs. He picked up 11 wickets for 128 runs in the match.  In 1995 English cricket season Kumble played for Northamptonshire and was the leading wicket taker with 105 wickets at the average of 20.40. He was the only bowler to take more than 100 wickets during that season. His best performance came against Hampshire in a drawn match in County Championship, picking up 13 wickets for 192 runs. This performance in the English county cricket was noted by Wisden as they named him one of their five Cricketers of the Year in 1996.

When was his international debut?
He made his ODI debut against Sri Lanka at Sharjah in the Austral-Asia Cup on 25 April 1990.