Superior Court, District Court, Court of Appeals and Supreme Court judges get picked by the Governor and then the run for retention in the general elections.
When a bench opens up, interested attorneys send their name into the Alaska Judicial Council. The Council sends out a questionnaire to the members of the bar and the attorneys grade the applicants and make comments. The highest graded applicants are then interviewed by the Judicial Council and the Council then sends a list of names to the Governor. There is an opportunity for public comment before the names are sent up. The Governor can pick a name from the list or reject the entire list but s/he cannot appoint someone is not on the list.
(Magistrates and Masters, however, are state employees. They apply for the job and go through the same process any other employee would.)
Periodically, the judges run for retention. In my 30 years, I've never heard of a judge who lost the election after the Judicial Council recommended retention. However, from time to time, judges do lose the election and that's because, usually, that judge has made a lot of people mad. Mad enough to make sure everyone knows to vote against the judge. In addition, there are people who may be following the Council's recommendation. Attached is this year's recommendation: