database.js

var mysql = require('mysql');
var connection = mysql.createConnection({
  host : 'localhost',
  user : 'node-test',
  password : '',
  database : 'node_test'
});

exports.open = function (callback){
 connection.connect(function(err){
  callback(err, connection);
 });
}

// USAGE
var db = require('./database.js');

db.open(function (err, con) {
  if (err) return;
  // ...
});

index.js

var user = require('./user.js');

var results = user.all();

console.log(results);

user.js

var db = require('./database');
var connection = db.open();

exports.all = function(){
 connection.query('select * from user', function(err, rows){
 if(err){
   console.log(err);
 } else {
   console.log('Query successfull');
 }
 });
}