How do I use OpenDKIM with multiple domain names on a single server?

You'll need to set up a KeyTable with a separate line for each selector/domain/keyfile. It would look like this:

default._domainkey.example1.com example1.com:default:/etc/mail/dkim/keys/example1.com/default
default._domainkey.example2.com example2.com:default:/etc/mail/dkim/keys/example2.com/default
default._domainkey.example3.com example3.com:default:/etc/mail/dkim/keys/example3.com/default

then a SigningTable to determine who can sign on each domain:

*@example1.com default._domainkey.example1.com
*@example2.com default._domainkey.example2.com
*@example3.com default._domainkey.example3.com

Here's an easy How-To for setting it up:

http://stevejenkins.com/blog/2010/09/how-to-get-dkim-domainkeys-identified-mail-working-on-centos-5-5-and-postfix-using-opendkim/