How do you break up with a co-worker?

A reader, Greg, would like advice on a dating dilemma.  He began dating a co-worker a few months ago but  she isn’t a good match for him.  He believes that she feels the same way about him, so the break up should not be surprising.  He wants to know how do you break up with someone you are dating if you work together?

To further complicate things, Greg wants to ask another co-worker out on a date.  Is it a good idea to date more than one person in the workplace?  I dated at work once and it never got messy or awkward. We were always very discreet, though.   I don’t think anyone knew we were a couple.  This was helpful when things ended, I didn’t have to really deal with all he opinions.