Take a look at /etc/inetd.conf and find the following lines:
# POP and IMAP mail servers
# Post Office Protocol version 3 (POP3) server:
pop3 stream tcp nowait root /usr/sbin/tcpd /usr/sbin/popa3d
# Internet Message Access Protocol (IMAP) server:
imap2 stream tcp nowait root /usr/sbin/tcpd imapd
The pop3 and imap2 lines will be commented. Just uncomment them, restart inetd (/etc/rc.d/rc.inetd restart) and you're good to go. Since you did a full install, you won't have to worry about uw-imapd and popa3d being installed.
As for setting up Sendmail with Slackware, it's ridiculously easy. Since you did the full install, that'll be installed, too. Relaying is turned off by default. In order to enable relay of trusted clients, just edit /etc/mail/access to add the IP addresses (or IP range) that you want to allow relay for.
Here's what mine looks like:
root@alice:/etc/mail# cat access
The .X.1 line is my firewall. Because I'm forwarding port 25 to the mail server, and I *don't* want to allow outside relay, I've put that line in to allow connections from .1, but to deny relaying. Since I'm running as the primary MX for my two domains, I need to allow connections from the outside to my mail server.
For everything else on the network, I'm allowing relaying.
Be *very* careful about who you allow to relay mail, because it's a great way to get yourself blacklisted.
Once you've set up the /etc/mail/access file, cd to /etc/mail and run "make". Then restart sendmail (/etc/rc.d/rc.sendmail restart), and you're up and running.