How do I use Font Awesome on a form submission button?
I normal replace search button value into Fontawesome Unicode code. 

In your css just define fontawesome font-family.

E.G  In your own module call hook_form_alter()

if($form_id = 'search_block_form'){
  $form['actions']['submit']['#value'] = decode_entities('&amp;#xf002;');


}

remeber use decode_entities() to parse the Unicode code.

CSS 

.block-search input[type="submit"]{
  border: 0;
  font-size: 1.3em;
  vertical-align: top;
  margin-left: -45px;
  font-family: 'FontAwesome';
}


You should get search icon on button and place inside of your text input field.

ref. Font-Awesome cheatsheet