How do I switch to a new jQuery UI tab programmatically?

@Aaron Sherman already answered your question. Here is the detailed step.

Here is JS part of the code:

$(document) .ready(function() {
    $("#tabs").tabs(); 
    $(".btnNext").click(function () {
            $( "#tabs" ).tabs( "option", "active", $("#tabs").tabs('option', 'active')+1 );
        });
        $(".btnPrev").click(function () {
            $( "#tabs" ).tabs( "option", "active", $("#tabs").tabs('option', 'active')-1 );
        });
});

Here are the "a href" tags to be added in your tabs div

Example:

<div id="tabs-1">
<a class="myButton btnNext" style="color:white;">Next Tab</a>
</div>
<div id="tabs-2">
<a class="myButton btnPrev" style="color:white;">Previous Tab</a>
<a class="myButton btnNext" style="color:white;">Next Tab</a>
</div>
<div id="tabs-3">
<a class="myButton btnPrev" style="color:white;">Previous Tab</a>
</div>

Try changing your code to this:

var $tabs = $('#tabs').tabs({ selected: 0, disabled: [1,2] }); 
$("#addstudent").click(function(){
   $tabs.tabs('enable', 1).tabs('select', 1).tabs('disable', 0);        
}); 
$("#confirm").click(function(){
    $tabs.tabs('enable', 2).tabs('select', 2).tabs('disable', 1);    
}); 

JSBin Example

For jQuery UI 1.9+, the select method has been deprecated in the API. In 1.9+, you need to use option and active, instead.

From the documentation:

Old API:

// Activate the third tab (in a zero-based index)
$( "#tabs" ).tabs( "select", 2 );

New API:

// Activate the third tab (in a zero-based index)
$( "#tabs" ).tabs( "option", "active", 2 );