While guards change positions every two hours, the main event for visitors is the changing of the entire guard at noon, when the guards are relieved by new guards coming from Rosenborg Castle. The event is called the "Vagtparade" in Danish.
The main task of the royal guard in Copenhagen is to protect Denmark's royalty, mainly Queen Margrethe II. The guards themselves are not a tourist attraction and will not talk to sightseers - they are working, after all. Please don't try to make them talk to you.
Note that the changing of the guard will be accompanied by music if the Queen or other royal family members are at Amalienborg Palace.