When you renew by phone or mail, you will be sent a voucher similar to the kind you get when purchasing a brand new AP. That voucher along with your old pass will need to be exchanged at a Guest Relations location when you go to WDW.
If you renew while you are at WDW, you just give them your old pass and they will give you back your activated renewed pass.
As Carol said, don't rely on getting a notice in the mail. The odds are more likely that you won't. Keep track of it yourself and phone in the renewal during June.
You can also just wait and do it in person when you go in July. The Guest Relations CM has great latitude in renewing passes past their expiration date. They will still backdate the renewal to your old expiration date and charge you the full amount.