Here is a regex that will validate 99% of emails
/^(("[\w-\s]+")|([\w-]+(?:\.[\w-]+)*)|("[\w-\s]+")([\w-]+(?:\.[\w-]+)*))(@((?:[\w-]+\.)*\w[\w-]{0,66})\.([a-z]{2,6}(?:\.[a-z]{2})?)$)|(@\[?((25[0-5]\.|2[0-4][0-9]\.|1[0-9]{2}\.|[0-9]{1,2}\.))((25[0-5]|2[0-4][0-9]|1[0-9]{2}|[0-9]{1,2})\.){2}(25[0-5]|2[0-4][0-9]|1[0-9]{2}|[0-9]{1,2})\]?$)/i
It looks a bit cryptic, but it works! As Damovisa stated in the comments, it is easier to use PHP's filter_var($email, FILTER_VALIDATE_EMAIL)
function.
Note if you are validating the email before you send it to PHP (for an ultra speedy validation), you will need to use a regex as there are no built in functions inside JavaScript to do this for you.
If you do use AJAX, you should have it return a success or error report using JSON.
The jQuery library can help you out a lot when using AJAX, but it's still important to understand how it works.