How are NHL games scheduled?

They play within division and conference, mostly, and fewer games against the other conference.

Within the division, 4 games × 6 opponents + 5 games × 1 opponent
Within Conference, Non-divisional 3 games × 7 opponents
Inter-conference 2 games × 16 opponents

While @zenvelo is correct on the details, the bigger picture is that there is sophisticated scheduling software that takes the rules into account, makes sure that certain rivalries are maintained, looks at the calendar, and comes up with the full schedule.

Baseball, football, basketball – all use some variation of the scheduling software. Baseball’s is most complex, because of the sheer number of games (162) and the cross-league play, which changes from year to year.