I'll post a few links here for you to peruse. Some use sendmail, some use postfix, but the gist is some walkthroughs for IMAP on Slackware using Dovecot.
I hope it helps
And this last one is neat because is discusses setting it all up while bridging the differences between doing it under Solaris or Slackware:
I would recommend that you use http://slackbuilds.org
and get your slackbuilds and compile create your own packages, instead of compiling from source as some of the walk-throughs show.
Other than that, perhaps one of the most important aspects of the LQ links is where the problems arose and how they were corrected, so you can avoid those pitfalls.
The differences between Slackware 13.0, 13.1, 13.37, and 14.0 should be minor, but pay closer attention when anything references something that is <= Slackware 12.
It should be a wealth of info that you can develop your own tutorial or howto from, so that folks in the future can benefit from your experience.
There's also just one more thing I often recommend to people that is absolutely wonderful, and that is:
This totally rocks for a couple of reasons. First, because you can operate totally offline as if you're online so you don't have to tell your clients to operate in offline mode or use up additional storage for each of your clients - just have OfflineIMAP do that for you.
Second, have all of your filtering and such there, so that you don't have to do it in each of your clients (and further, forget which of your clients had that filter applied).
You can install OfflineIMAP on your server, and have another slaved installation on each of your local workstations to make sure that all of your mail is available as if it were online even when you're not, and all of your filtering and sorting can be managed from one central location.
IMNSHO that's a totally kewl win/win situ