Class methods in node.js

I've been trying for the last hour to write a user module for passport.js with the findOne, findOneOrCreate, etc. methods, but can't get it right.

User.js

var User = function(db) {
  this.db = db;
}

User.prototype.findOne(email, password, fn) {
  // some code here
}

module.exports = exports = User;

app.js

User = require('./lib/User')(db);
User.findOne(email, pw, callback);

I've been through dozens of errors, mostly

TypeError: object is not a function

or

TypeError: Object function () {
  function User(db) {
    console.log(db);
  }
} has no method 'findOne'

How do I create a proper module with these functions without creating an object/instance of User?

Update

I went over the proposed solutions:

var db;
function User(db) {
  this.db = db;
}
User.prototype.init = function(db) {
  return new User(db);
}
User.prototype.findOne = function(profile, fn) {}
module.exports = User;

No luck.

TypeError: Object function User(db) {
  this.db = db;
} has no method 'init'