You can add an onclick function to your submit button, but you won't be able to submit your function by pressing enter. For my part, I use this:
<form action="" method="post" onsubmit="your_ajax_function(); return false;">
Your Name <br/>
<input type="text" name="name" id="name" />
<br/>
<input type="submit" id="submit" value="Submit" />
</form>
Hope it helps.