thing.js

function Thing(prop) {
  this.prop = prop;
}

Thing.prototype.toString = function() {
  return "My prop is: " + this.prop;
};

module.exports = function (opts) {
  return new Thing(opts);
}

module.exports.Thing = Thing;

usage.js

// Option one:
var Thing1 = require("./thing").Thing;
var thing1 = new Thing1("foo");
String(thing1) // "My prop is: foo"

// Option two:
var thing2 = new(require("./thing"))("bar");
String(thing2) // "My prop is: bar"