Edit in JSFiddle

<div id='messagesDiv'></div>
<input type='text' id='nameInput' placeholder='Name'>
<input type='text' id='messageInput' placeholder='Message'>

var myDataRef = new Firebase('https://dya872np1ze.firebaseio-demo.com/');
$('#messageInput').keypress(function (e) {
    if (e.keyCode == 13) {
        var name = $('#nameInput').val();
        var text = $('#messageInput').val();
        myDataRef.push({name: name, text: text});
        $('#messageInput').val('');
    }
});
myDataRef.on('child_added', function(snapshot) {
    var message = snapshot.val();
    console.log(message);
    displayChatMessage(message.name, message.text);
});
function displayChatMessage(name, text) {
    $('<div/>').text(text).prepend($('<em/>').text(name+': ')).appendTo($('#messagesDiv'));
    $('#messagesDiv')[0].scrollTop = $('#messagesDiv')[0].scrollHeight;
};