How do you write a constructor function?

A constructor is an ordinary function you call with new. Convention capitalises the name so readers know it is meant to be used that way — JavaScript itself does not enforce it.

function Person(name, age) {
  this.name = name;
  this.age = age;
}

Person.prototype.greet = function () {
  return `Hi, I'm ${this.name}`;
};

const p = new Person("Mai", 30);
p.greet();          // "Hi, I'm Mai"

Methods go on prototype, not inside the constructor. Defining this.greet = function... would create a separate copy for every instance; on the prototype there is one copy shared by all of them.

What new does

Four steps: create an empty object, set its prototype to Person.prototype, run the function with this bound to that object, and return it automatically unless the function returns a different object explicitly.

The trap

Forgetting new fails quietly:

const bad = Person("Mai", 30);   // undefined, and `this` was undefined inside

In strict mode or a module, this.name = name throws; in sloppy mode it writes to the global object instead. You can guard against it:

function Person(name) {
  if (!new.target) return new Person(name);
  this.name = name;
}

Prefer class in new code

class Person {
  constructor(name) { this.name = name; }
  greet() { return `Hi, I'm ${this.name}`; }
}

This is the same prototype machinery with clearer syntax, and it removes the trap above — calling a class without new throws a TypeError immediately. It also gives you extends, super and private #fields. Constructor functions are still worth understanding, because that is what you will meet in older code and what class compiles down to conceptually.