Dan, you've been given good advice so far. Make sure your legs are spread pretty wide and that the head of the dulcimer sits on your knee. Some people use that shelf liner/carpet pad stuff on their laps, but others claim that the material can mark the finish of your dulcimer.
Although some traditionalists frown upon using straps, I had a horrible problem with my dulcimer moving around until I installed strap buttons and began using a strap around my lower back. The dulcimer immediately became "mine." You can make your own strap, of course, and Strumelia has a nice video about how to do that at her noter/drone blog (scroll down to the very lower bottom of this page). Carrie is right that any adjustable guitar strap will also work, but my preference is the quick release dulcimer strap that Sue Carpenter designs and sells. I have one on each of my dulcimers now.

And I have yet to name my baritone dulcimer, though the lower range might indicate a male voicing. I'm thinking Otis.