There are two basic ways to keep score in beach volleyball. The first way is called rally scoring.
The way that works is that, every time a rally ends, one team gets a point whether they served or not.
The other way is called side out scoring that is the classic, older way of keeping score. The way that works is the only way a team can score a point is if they serve the ball and they win the point. Side out scoring is considered old school scoring and isn't used often these days.
Internationally and domestically, rally scoring is the typical way to score. Every time a rally ends in rally score, you get a point. You get a point when the other team makes a fault or you get a kill or ace.
When you get a kill, it means you hit the ball and the other team is unable to dig it. When you get an ace it means that the other team is unable to pass your serve. An ace is off of a serve and a kill is off a hit. Both of those result in a hit for the offensive team.
Games are typically played to 21 points. You switch sides every 7 points. A match is the best 2 out of 3 games. If one team wins the first game to 21 and the other team wins the second game to 21 then a tie breaker game is played to 15. That's how you keep score in beach volleyball.