To be able to fetch your emails from any mail client, you need to run a POP/IMAP server. We'll use dovecot, parts of which were already installed previously (to allow postfix to identify users).
aptitude install dovecot-imapd dovecot-pop3d
Congratulations, you now already have a functional POP/IMAP server running.
It is not quite complete though. We configured postfix to use Maildir instead of mbox, but dovecot comes with a default configuration of mbox. Thus, we need to adapt the file /etc/dovecot/conf.d/10-mail.conf, in particular the line defining the mail_location - just comment out the existing entry and add:
mail_location = maildir:~/Maildir
Don't forget to restart dovecot after this modification.
For fine-tuning though - you may want to allow logging in not only with the useraccount name, but also with username@domain, i.e. the basic email address. In this case, you can edit /etc/dovecot/conf.d/10-auth.conf and set the auth_realms parameter, as well as the auth_username_format:
auth_realms = hellsnet.lu auth_username_format = %n
The auth_realms are the possible domains. If a full email address is provided, the auth_username_format will drop the domain part and try authenticating the remainder as username. Obviously, that won't work for mail aliases - this would need a proper directory service (such as LDAP), which might be a tad overkill for a personal server.