• HTML
• CSS
• JS

HTML

<div>
    <h3>Contador de Carácteres</h3>
    <textarea rows="10" id="texto"></textarea>
    <button onclick="contar()">Contar</button>
    <button onclick="restaurar()">Restaurar</button>
    <input type="text" id="num" style="width:100px;">
</div>

CSS

body{
    font-family:sans-serif;
}
div{
    width:300px;
    margin:0px auto;
}
textarea{
    width:100%;
    background:#85c1e9;
}
h3{
    margin:10px 0px;
}

JS

var texto = document.getElementById("texto");
var num   = document.getElementById("num");

function contar(){
    var text  = texto.value.length;
    num.value = text;
}

function restaurar(){
    texto.value = "";
    num.value   = "";
}