The Round of 16 of the World Cup was full of extra time games, but they've been scarce since. Unlike group stage games, which can end in a draw, games from that point onwards need a winner and a loser. So if the match is tied in regulation, it has to continue.
Extra time is used to settle ties after 90 minutes, with the two teams playing 30 more minutes in two 15-minute periods. Stoppage time is added on at the end of each of those halves, just like it is during regulation. A penalty shootout occurs if the two teams are still tied after that 30 minute extra time period.
The 'golden goal' rule is not in effect, meaning that the game does not end when one team scores a goal. No matter what, they have to play the entire 30 minutes of extra time. So if one team scores, the other team has the rest of extra time to match them, and they win the match if they score twice.
Penalty kicks are a best of five shootout alternating between the two teams. They end when one team is no longer mathematically able to match their opponent's result through five rounds; if one team scores their first three penalties and the other team misses their first three, the shootout is over. If there's a tie at the end of five rounds, they go to sudden death, where each team takes a penalty until one team misses and the other scores in the same round.