Edit in JSFiddle

$(function() {
    var navHeight = 0;
    $('nav a').on("click", function() {
        var hash = this.hash,
            target = $(hash).offset().top - navHeight;

        $('html,body').stop().animate({
            scrollTop: target
        }, 1500, function() {
            window.location.hash = hash;
            $(window).scrollTop($(hash).offset().top - navHeight);
        });
        return false;
    });
    $(window).on("scroll resize", function() {
        $('nav a').each(function() {
            var section = this.hash,
                sectionTop = $(section).offset().top,
                windowTop = $(window).scrollTop() + navHeight,
                sectionEnd = sectionTop + $(section).outerHeight() - navHeight;
            if ((windowTop >= sectionTop) && (windowTop <= sectionEnd)) {
                $(this).closest('nav').find('.active').removeClass('active');
                $(this).addClass('active');
            } else {
                $(this).removeClass('active');
            }
        });
    }).trigger("scroll");

    // Scroll to section ID based on window.location.hash
    // The 'navHeight' was only used to add the jump spacing.
    if (window.location.hash) {
        var hash = window.location.hash;
        $(window).scrollTop($(hash).offset().top - navHeight);
    }

});

<nav>
    <ul>
        <li><a href="#home">Home</a></li>
        <li><a href="#about">About</a></li>
        <li><a href="#portfolio">Portfolio</a></li>
        <li><a href="#contact">Contact</a></li>
    </ul>
</nav>
<section id="home"><h2>Welcome!</h2><p>Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat.</p></section>
<section id="about"><h2>About</h2><p>Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat.</p></section>
<section id="portfolio"><h2>Portfolio</h2><p>Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat.</p></section>
<section id="contact"><h2>Contact</h2><p>Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat.</p></section>

body {
    margin:0 0;
    padding:0 0;
}

h2 {
    font:bold 20px Times,Serif;
    margin:0 0 15px;
}

nav {
    position:fixed !important;
    position:absolute;
    top:0;
    bottom:0;
    left:0;
    z-index:77;
    width:120px;
    background-color:black;
}

nav ul {
    margin:0 0;
    padding:0 0;
    overflow:hidden;
}

nav li {
    list-style:none;
    margin:0 0;
    padding:0 0;
}

nav a {
    font:bold 11px/30px Arial,Sans-Serif;
    color:white;
    display:block;
    padding:0 15px;
    text-decoration:none;
}

nav a:hover {color:#ccc;}
nav a.active {background-color:darkblue;}

section {
    padding:30px;
    border-top:2px solid darkred;
    height:1000px;
    margin:0 0 0 120px;
}

#home {background-color:green;}
#about {background-color:skyblue;}
#portfolio {background-color:gray;}
#contact {background-color:orange;}