This can be easily done with jQuery, a Javascript Library. To use the features of jQuery, you must download the source code and include it in your HTML <head>
tag.
<head>
<script type="text/javascript" src="jQuery.js"></script>
</head>
For a smaller file-size version of jQuery, use this source code.
Now, to trigger the submit on "Enter":
$('.input').keypress(function(e) {
if(e.which == 13) {
$(this).blur();
$('#submit').focus().click();
}
e.preventDefault();
});
... and I would further modify your <form>
by adding some classes and ids, but for the above suggestion, make sure to add the class "input" and the id "submit":
<form>
<button>first button</button>
<button>second button</button>
<input type="text" class="input">
<input type="submit" id="submit">
</form>
Let me know if that works. I hope this helps.