Which election takes place first the primary election or the general election?

The two methods for an American political party to choose a presidential candidate to represent it are the caucus and the primary. They're very similar, and have the same basic result. The Constitution sets the basic rules for how elections work, and then lets each state make their own laws to decide how to run the elections within that basic framework.

A primary is just like a regular election. Everyone who votes in it goes to their precinct polling station and votes for the candidate they prefer. The state and local governments run the primary, and have rules governing it, just like a regular election.

A caucus is similar, except that instead of going to a local precinct, each voter goes to a special meeting held by the party. The party itself runs the meeting, and conducts the voting; the state/local government is not involved, and state election laws (if any) do not have to be followed.

Each caucus or primary results in delegates being chosen to vote for the party's candidate at the party's convention. Different states have different rules for how these work in the nomination process. Most states have "binding" rules that require the delegates to vote only for who they were chosen to vote for; the delegate can't be "faithless" and choose to vote for someone else. Additionally, most states are "winner take all"- the person who wins the most votes in the state gets all of that state's delegates, even if the person only won by a single vote.