the person who made the last aggressive action in a hand is the first to showdown..... ie after the river, the person who bets or raises last and gets called should be first to show.
Once he has shown his cards, the other(s) who called can choose to muck their cards. HOWEVER, anyone who is still in the hand at Showdown can theoretically asked to see those mucked cards, although this is considered poor etiquette.
When a hand goes check/check on the river, most card rooms will insist that all hands are shown at showdown
When a player who should showdown first after the river chooses to just muck, the other person is the winner by virtue of being the only player left with a live hand, but still has to show their hand to be able to claim the pot (another rule that varies from one cardroom to another though)
