This is the error I get in my log (/var/log/mail.log) every time I try to connect with a client. I've followed the certificate generation as per the tutorial here:

https://www.digitalocean.com/communi...r-with-dovecot

Everything seems to be working fine apart from being able to establish a connection due to the certificate issues. I don't have any experience dealing with certificates, can anyone help me?

That seems fairly clear.

If you're sure you followed the instructions correctly, then try some different instructions.

These are the commands I used. The second points to the mail.key file. Does it look right?

both are right, but you need to choose one. the first generates a self-signed certificate (and a key). the second generates a certificate signing request (and a key).

if you ran both commands, then the key generated with the second command overwrote the first one.

if you're just experimenting, generate a self-signed certificate.

How would I go about generating a certificate or obtaining one from a CA and generating a key from that? In school we very loosely covered key and certificates, and even then it was all automated in Exchange.

the first command in your post #3 (above) generates a key and a self-signed certificate. the key is saved in /etc/ssl/private/mail.key, and the certificate in /etc/ssl/certs/mailcert.pem. that should be enough to test your services.

if you need a certificate signed by a reputable CA, you'd need to run the second command in that post, instead. that would generate a key and CSR. you'd then submit the CSR (not the key), along with a fee, to the CA for signing.

quick review: the "key" mentioned above is your private key, which you don't divulge to anyone. the "certificate" is your public key together with a "signature" from a CA attesting to your identity (i.e. attesting that the public key belongs to the you).

in the case of a self-signed certificate, you use your own private key to "sign" the certificate.