How to put an image in front of a button?

Edit the structure. If the button comes after from input there is no reason to put it before in HTML.

<form action="newsletter.php" method="post" class="content-form clearfix" id="newsletter-form">
  <input id="newsletter" type="email" name="newsletter" placeholder="Fique por dentro de nossas ofertas">
  <input type="submit" class="button" name="button" id="button" value="Enviar">
  <img src="imagens/icone-facebook.png" width="29" height="29">
</form>

To adjust your layuot and make room for img to be right:

.one-half {
  width: 80%;
  max-width: 500px;
}

The input and the button are aligned with float: left and img with float: right .

#newsletter-form input#newsletter {
   float: left;
   width: 360px;
   margin-right: 10px;
   display: inline;
}

#newsletter-form input.button {
  float: left;
  margin-right: 0;
  margin-bottom: 5px;
  display: inline;
}

#newsletter-wrap img {
  float: right;
  display: inline;
}

Result:

If you want to bring the facebook icon closer to the Send button, just add margin-right to img and adjust until you get to where you want.

Image is out of form and as form is block so image has to be within tag form , try to set tag img within form and add your css:

#newsletter-wrap img{
    display:block;
    float:right;
}