Learn English – Much or Many for Money

People is usually the plural form of person:

One person, two people, three people, ...

What you'll notice here is:

• People is countable.
• People is plural, even though there's no -s suffix.
• The singular form is always one person, never *one people.
• The indefinite forms include a person and people.

Here are a few more details you can safely ignore:

This is called suppletion, and it's much like how we say went as the past form of go, even though went was originally a different word (the past form of wend).

The plural persons exists too, but it's limited to a few formal legal contexts. In everyday life, people use people as the plural form and ignore the word persons entirely.

And now, here are some details you shouldn't ignore:

People isn't just used as the plural of person. It's also used as a separate word meaning "the persons living in a country and sharing the same nationality" (Collins). And when it's used in this sense, both the singular and plural forms look different:

One people, two peoples, three peoples, ...

Although these are grammatical, we're not terribly likely to count peoples this way. This term is more likely to be used in phrases like the French people, the Navajo people, or the Native American peoples (note the plural, as there is more than one group of Native Americans).

You can tell the difference by how the word looks. If it's two people, it's the plural of person. If it's two peoples, it's referring to two groups of people, each of which has a distinct identity. And if it's one people, it must be referring to a group.

But most of the time, people is the plural of person.

For the same reason "the pen" in Spanish is "la pluma", while "the pencil" is "el lápiz" instead of "la lápiz": it sounds more natural to native speakers (as StoneyB mentioned in the comment, we're 'voting' on how to use these words).

Note that if you mix these up you'll probably get a few funny looks, but you won't be misunderstood.