In jQuery, you can use event.which==13. If you have a form, you could use $('#formid').submit() (with the correct event listeners added to the submission of said form).
$('#textfield').clickkeyup(function(event){
if(event.which==13){
$('#submit').click();
}
});
$('#submit').click(function(e){
if($('#textfield').val().trim().length){
alert("Submitted!");
} else {
alert("Field can not be empty!");
}
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<label for="textfield">
Enter Text:</label>
<input id="textfield" type="text">
<button id="submit">
Submit
</button>