Auto-reply from the old email that says, "This email address will stop working in {n} days. Please update your address book with <new email address>" Ideally only reply to those in your address book so spammers do not get the new address so easily.

Also CC your new email address from the old one in an email to everyone you care about with "I have updated my email address to <new email address>" so it's easier for them to add it.