Theory is that everything works automatically. Practice sometimes differs.
I suppose that you are talking about S/MIME and X.509 certificates. With S/MIME, when you send an email:
- The email is encrypted with the public key of the recipient, so you have to know the current recipient's certificate.
- The email is signed with your private key and the signature format normally includes a copy of your own certificate.
Thus, other people learn your current certificate when you send signed emails to them. Once they received such an email, they can send encrypted emails to you. If these people also signs their own emails, then you learn their certificates as well, and you will thereafter be able to send encrypted emails to them.
When you get your new certificate, your correspondents don't know it yet; they just know the previous one. When your old certificate expires, they will cease to be able to send encrypted emails to you. But, as soon as you send them a signed email, they will learn your new certificate and everything will be fine again. Storage of copies of the certificates of other people is supposed to be done automatically by your emailing software, so there is never some manual import to do. At least when everything works fine.
If you want people to be able to send you encrypted emails without first receiving a signed email from you, then you can put a copy of your certificate (not your private key, of course) on your personal Web site, Facebook profile, or anything similar.
(In the dreams of the original X.509 designers, certificates for everybody would be found at any time in a worldwide, shared directory called the Directory, with an uppercase D. This is why the main identity in an X.509 certificate is a Distinguished Name: this is a hierarchical path within the Directory. But this never happened: the Directory remained a purely theoretical beast.)