My honest solution

function Question(question, firstAnswer, secondAnswer, correctAnswer){
    this.question = question;
    this.firstAnswer = firstAnswer;
    this.secondAnswer = secondAnswer;
    this.correctAnswer = correctAnswer;
}

function Quiz(){
    this.questions = [];    
    this.score = 0;
    this.currentQuestion = 0;
    //quiz always starts with at least 1 question
    this.progress = 1;
}
// adds question to quiz
Quiz.prototype.addQuestion = function(question){
    this.questions.push(question);
}
// calculate quiz score
Quiz.prototype.updateScore = function(){
    this.score++;
}
// get the users answer
Quiz.prototype.getAnswer = function(buttonClickId){
    var userAnswer;
    var quizQuestion = this.questions[this.currentQuestion];
    if (buttonClickId == "guess0"){
        userAnswer = quizQuestion.firstAnswer;
    }
    if (buttonClickId == "guess1"){
        userAnswer = quizQuestion.secondAnswer;
    }
    return userAnswer;
}
// check the users answer
Quiz.prototype.checkAnswer = function(buttonClickId){
    if (this.quizProgress()){
        var userAnswer = this.getAnswer(buttonClickId);
        var quizQuestion = this.questions[this.currentQuestion];
        if (userAnswer == quizQuestion.correctAnswer){
            this.updateScore();
        }
        this.currentQuestion++;
        this.progress++;    
    }
}
// check the quiz status
Quiz.prototype.quizProgress = function(){
    if (this.currentQuestion != this.questions.length){
        return true;
    } else {
        return false;
    }
}
// load quiz
Quiz.prototype.load = function(questionEl, firstAnswerEl, secondAnswerEl, progressEl, quizEl){
    if (this.quizProgress()){
        questionEl.innerHTML = this.questions[this.currentQuestion].question;
        firstAnswerEl.innerHTML = this.questions[this.currentQuestion].firstAnswer;
        secondAnswerEl.innerHTML = this.questions[this.currentQuestion].secondAnswer;
        progressEl.innerHTML = "Question ";
        progressEl.innerHTML += this.progress;
        progressEl.innerHTML += " of ";
        progressEl.innerHTML += this.questions.length;
    } else {
        quizEl.innerHTML = "<h1>Gamer Over!</h1>";
        quizEl.innerHTML += "<h3>You score is: " + this.score;
        quizEl.innerHTML += "</h3>";
    }
}

// create quiz
var quiz = new Quiz();
// create questions
var question1 = new Question("What color is the sky?", "Blue", "Red", "Blue");
var question2 = new Question("What is the current year?", 2016, 2017, 2017);
// add questions to quiz
quiz.addQuestion(question1);
quiz.addQuestion(question2);
// get quiz elements
var question = document.getElementById("question");
var firstAnswer = document.getElementById("choice0");
var secondAnswer = document.getElementById("choice1");
var progress = document.getElementById("progress");
var quizWrapper = document.getElementById("quiz");
// load quiz content first time
quiz.load(question, firstAnswer, secondAnswer, progress, quizWrapper);
// listen to answers
var guess0 = document.getElementById("guess0");
guess0.onclick = function(){
    quiz.checkAnswer(this.id);
    quiz.load(question, firstAnswer, secondAnswer, progress, quizWrapper);
}
var guess1 = document.getElementById("guess1");
guess1.onclick = function(){
    quiz.checkAnswer(this.id);
    quiz.load(question, firstAnswer, secondAnswer, progress, quizWrapper);
}