NodeJS using a class from another file

I think you want a Function constructor named Champion (a prototype or blue-print like classes in other programming languages like Java).

As an alternative I would suggest you to learn ES6 way of writing classes which is similar to that of Java.

You can achieve that by adding all the variables or methods to the this variable inside the Function Constructor so that you can access them using an object created using the 'new' keyword i.e make them Class members or methods.

In your case,

function Champion(champName) {
    //Some code

    this.most_frequent_completed_build = NULL;

    //Rest of code
}

module.exports = Champion;

Just make sure whenever you try to access Class variables always use this.variable_name like this.most_frequent_completed_build.

So when you create a new object of this Class in main app you will be able to access all Class members and methods.

const Champion = require("./championgg_webscraper_cheerio.js");

var temp = new Champion("hello");
console.log(temp.most_frequent_completed_build);

You are exporting a function

All you have to do is call that function like

var temp = Champion();

You can read more about new keyword here and here

    function Champion(champName) {
  //CHEERIO webscraping
  var cheerio = require('cheerio');
  //REQUEST http library
  var request = require('request');
  //url of the champion
  var url = "http://champion.gg/champion/Camille/Top?";
  var most_frequent_completed_build;
  var highest_win_percentage_completed_build;
  request(url,
    function(error, response, html) {
      if (!error && response.statusCode == 200) {
        var $ = cheerio.load(html);
        var final_build_items = $(".build-wrapper a");
        var mfcb = [];
        var hwpcb = [];
        for (i = 0; i < 6; i++) {
          var temp = final_build_items.get(i);
          temp = temp.attribs.href;
          //slices <'http://leagueoflegends.wikia.com/wiki/> off the href
          temp = temp.slice(38);
          mfcb.push(temp);
        }
        for (i = 6; i < 12; i++) {
          var temp = final_build_items.get(i);
          temp = temp.attribs.href;
          //slices <'http://leagueoflegends.wikia.com/wiki/> off the href
          temp = temp.slice(38);
          hwpcb.push(temp);
        }
        most_frequent_completed_build = mfcb;
        highest_win_percentage_completed_build = hwpcb;
      } else {
        console.log("Response Error: " + response.statusCode);
      }
    }
  );
  return {most_frequent_completed_build:most_frequent_completed_build};
};
module.exports = Champion;

    var temp = new Champion("hello");
console.log(temp.most_frequent_completed_build);