There's no real way to confirm an email really exist other than sending it an email and seeing if you get a bounce-back (And even then some domains have catch-all's configured so it may not actually be an email).
You can validate the format of it to make sure it looks vaguely like an email. To truly validate an email takes an ungodly complex regex (I've yet to see one that truly encompasses the scope), but a simple check that'll rule out most keyboard-mashing is pretty easy. I typically use:
^[A-Za-z0-9._%+-]+@[A-Za-z0-9.-]+\.[A-Za-z]{2,6}$
There's a lot of fake emails it will accept, but it does a reasonable job of forcing the user to enter something legitimate. Be wary if using a more complex regex that you don't accidentally ban any legitimate addresses, the email spec is very broad in what's allowed.
You could also try doing a DNS lookup on the host portion of the email (After the @) for an extra level of protection, but I'm not sure how much you'll get from this as you'll just force them to lie with a real domain name.