gistfile1.js

function getDay(callback) {
  
  request('http://www.timeanddate.com/', function date(error, response, html){
    
    if (!error && response.statusCode == 200) {
      var $ = cheerio.load(html);
      $('span#ij1').each(function(i, element){
        var dag = $(this).text();
        console.log(dag);
        
        //call the passed in function with dag as the first argument, getSChema is the callback
        callback(dag, getSchema);
      });
    };
    
  });
};

function getWeek(dag, getSchemaCallback) {
  request('http://ugenr.com/', function(error, response, html) {
    if (!error && response.statusCode == 200) {
      var $ = cheerio.load(html);
      $('span#ugenr').each(function(i, element){
        ugeNr = parseInt($(this).text().split(" ")[1]);
      });
      if (dag == "Saturday" || dag == "Sunday"{ //Depends on language of site
        var ugeNr = +1;
      };
    };
    
    getSchemaCallback(ugeNr);
  });
};

function getSchema(ugeNr) {
  
  request('http://domain/services/name.ashx?idx=randnum&week='+ugeNr, function (error, response, html) {
    if (!error && response.statusCode == 200) {
      var $ = cheerio.load(html);
      $('div#uge'+ugeNr).each(function(i, element){
        elevNavn = $(this).children('.titledata').text();
        console.log(ugeNr);
        console.log(elevNavn);
      })
    };
  });
};

getDay(getWeek);

you are calling getDay, and passing in the function getWeek as the callback, so getDay will call the getWeek function after it finishes it stuff, getWeek does the same thing for getSchema