There are many different ways that scoring can occur in the many sports that exist. A good way of keeping track of the numerous ways is to group sports into categories. The most notable and popular group of all types of sports are the basket/net sports. Another remarkable grouping of sports is the racquet sports. There is also a group that is prevalent as well and that is the target sports. Additionally, you have some sports that are just unique in their own respect; baseball, bowling, and football are all one of a kind just because there are no other sports that come close to them in terms of similarity.
The basket/net sports almost always count points scored when their spherical ball enters the basket/net. In every one of these sports, the only way in which to score is by putting the ball through the net. The basket in the very telling 'basketball' is the objective through which to put the ball in a game. It does not have a keeper and, in fact, the points count if the team on defense is caught "goaltending." There are one-point "free throws," earned if one is fouled, two-point "field goals", and three-point field goals shot from farther than the two-pointers.
In soccer, like basketball, the only way to score is by putting the ball into the net. The difference is that soccer has more players on the field and the field is bigger. One can either conventionally put the ball into the net during regular time, or if a foul is committed by the opposite team in the penalty area, the offensive team can shoot a free throw-like shot in which it is a free one-on-one with the goalkeeper. Soccer and basketball were the examples used because they are very popular and speak for the other net sports (e.g. lacrosse, hockey, etc.)
Racquet sports have a pretty rigid standard for scoring conventions. In these sports, which includes tennis, badminton, ping pong, and more, a point is scored when the other team cannot return the objective (i.e. tennis ball, shuttlecock, etc.). On the other hand, an offending team can give the defending team a point if they hit the objective out of bounds. These sports usually have no time limit, rather there is a score to be achieved to win, as opposed to basket/net sports, where time is a factor. I would include volleyball in this group because, even though there are no racquets, it has the exact idea of scoring that identifies with this group.
Target sports, such as darts, archery are a little more complicated. In short, the objective is to get as close to the target as possible. More points are allocated the closer one gets to the target.
Esports introduce even more ambiguity to a convention of scoring. There are many games that are all different in their own way. Usually, though, esports, similar to tennis, have an amount of rounds and one team needs to win more rounds in order to be victorious.
If one desires to read sports scores, there are different things to look for depending on the different sports about which one is reading. Generally, sports are two-sided, so to see who's winning, look at who has more points. Now golf is a sport that goes against this as it has more than two competitors, usually, and one wants the least number as a score. Other than golf, though, looking to see who has more points goes a long way when reading sports scores.
In football, the increments by which a team's score can increase is by 1,2,3, and 6. To score six, a team must get a touchdown, getting the ball to the other team's endzone. To score three, the ball must be kicked through the uprights (field goal). Scoring one is the same as scoring three, it just happens after a touchdown (extra point). Scoring two can happen in two ways. A two-point conversion is the option other than an extra point field goal after a TD. A safety is when a defense tackles the ball-carrier in the offense's own endzone.
There is only one plain way of scoring in softball/baseball. This is by bringing in a baserunner past home plate (the 4th base). The multitude of ways by which this "run" can be scored is vast. For example, one can hit a homerun and bat themself in, all the better if there are runners already on base. One can also get a base hit and then a runner who is on any of the bases can get batted in (a runner on 2nd or 3rd base is considered in "scoring position").
There is another group of sports that each have their own intricate scoring systems. In MMA, for example, points can be scored from taking an opponent down, striking, and more; even the amount of hurt in a competitor plays a role. There are usually judging systems for sports with complicated scoring systems. For these sports, sometimes an awe factor can even come into play. If a skateboarder does an impressive trick that has never been done before in competition, the judges can just say he wins, even if another contestant has more points.