How do I add class to the next element when I click the button?

You can use this:

$('button#anterior').click(function () {
    $('.minhaClasse').removeClass('minhaClasse').prev().addClass('minhaClasse');
    if (!$('.minhaClasse').length) {
        $('li:last').addClass('minhaClasse')
    }
});
$('button#proximo').click(function () {
    $('.minhaClasse').removeClass('minhaClasse').next().addClass('minhaClasse');
    if (!$('.minhaClasse').length) {
        $('li:first').addClass('minhaClasse')
    }
});

Example

Your solution proposal (using next and addClass ) is correct. Here is a simple example (without checking for boundary conditions - like the first or last element):

$(".selecionado")
    .removeClass("selecionado")
    .next()
    .addClass("selecionado");

Example in jsFiddle .

P.S. A solution (not necessarily the cleanest) to test the boundary cases would check at the end of the code if "someone" is selected and if not, choose one as default (the last one, if you want it " front, "or the first if you want it to" go around "). Examples:

if ( $(".selecionado").length == 0 )
    $("li:last").addClass("selecionado");

Stopping example , example giving the turn .

Something like this?

$('.next').on('click', function() {

    $('ul>li.active').removeClass('active').next('li').addClass('active');

});

$('.prev').on('click', function() {

    $('ul>li.active').removeClass('active').prev('li').addClass('active');

});

The path is the same, but beware the .next() takes the next element, ie:

<script>
  $('.primeira').next();
</script>
<div class="primeira"></div>
<div class="segunda"></div>

The script takes the object div segunda .

But if so,

<script>
  $('.primeira').next();
</script>
<div class="primeira"></div>
<div class="itens">
    <div class="segunda"></div>
<div>

The object takes the class itens and not the second. You would have to get .next() after using .children()

link

See if you understand logic.

$(document).ready(function(){
    var anterior  = $('.btnAnterior');
    var proximo   = $('.btnProximo');
    var itemLista = $('.lista li:first-child');
    var qtdItens  = $('.lista li').length;
    var itemNum   = 1;
    var itemAtual = 1;

    $.each('.lista li', function(){
        $(this).addClass('item'+itemNum);
        itemNum++;
    })        

    proximo.click(function(){
        $('item'+itemAtual).removeClass('classeRemovida');
        $('item'+itemAtual+1).addClass('classeAdicionada');
        itemAtual = itemAtual + 1;
    })

    anterior.click(function(){
        $('item'+itemAtual).removeClass('classeRemovida');
        $('item'+itemAtual-1).addClass('classeAdicionada');
        itemAtual = itemAtual - 1;
    })
});