The language you speak depends on the people you grew up with. In most games, players all speak common. Common is a convenient name for whichever language is universally spoken in your game's setting. Your GM may decide to give Common a less generic name. For instance, a medieval fantasy set in France may all speak French instead. Depending on the setting, your GM may rule that no common language exists, which leads to some interesting roleplay challenges between players who may not understand each other. In games that take place in the underdark, players may know Undercommon instead. Some communities, like those of gnolls and bugbears, can be fairly xenophobic. If you were raised in such a community, you may not actually have learned Common.
If you grew up in a community composed of primarily one ancestry, you might also know a language associated with that group. Such languages include Aquan, Dwarven, Elven, Gnome, Halfling, Orcish, Goblin, Catfolk, Gnoll, Ratfolk, or Lizardfolk. Kobolds do not have a language of their own, but many of them speak Draconic, the language of dragons. Many gnomes, due to their connection to fey, speak Sylvan fluently.
Creatures that come from split ancestry may speak languages from both their lineages. Tieflings often have an understanding of Infernal or Abyssal. Aasimar often find they intuitively know Celestial, even if they never learned it. Half-giants often understand giant, as well as another humanoid language. The same goes for half-elves, half-orcs, and others.
The languages you learn from the community you were raised in (along with common and any class-based languages) are considered your primary languages. You always begin play knowing these fluently. Depending on your intelligence, you may have proficiency in a number of secondary languages. The maximum number of secondary languages you can learn is equal to your intelligence bonus, but you should work with your GM to determine how many of these (if any) you might know when you start.
Generally, secondary languages should make sense with your backstory. If the community you grew up in had significant contact with another community (whether enemies or friends) they may be able to speak each other's languages. For instance, if the elven community you grew up in has extensive contact with fey creatures in the wild, you might also know Sylvan as a secondary language. Likewise, it's also common for members of goblinoid or orcish communities to speak each other's languages.
The following is a quick overview of some secondary languages that are most common.