State Government
(1) Every High Court Judge is appointed by the President, holding office (for a permanent Judge) until age 62. A Judge may resign by writing to the President, be removed as a Supreme Court Judge would be (Article 124(4)), or vacate office on being appointed to the Supreme Court or transferred to another High Court. (2) A person is qualified if a citizen of India who has held judicial office in India for at least 10 years, or been a High Court advocate for at least 10 years. (3) Any dispute about a Judge's age is decided by the President after consulting the Chief Justice of India, finally.
This mirrors Article 124 (Supreme Court Judges) at the state level, including the same demanding removal process. IMPORTANT: like Article 124, the printed text says High Court Judges are appointed "on the recommendation of the National Judicial Appointments Commission" - but that Commission (and the 99th Amendment creating it) was struck down by the Supreme Court as unconstitutional in October 2015. High Court judges, in practice, continue to be appointed through the restored collegium system, not through the NJAC process this article's text describes.
Just as with Supreme Court appointments, every High Court judge appointed since late 2015 has gone through the collegium recommendation process, not the NJAC process the Constitution's printed text still describes.