I usually tune mine G-D-DD (bass to treble), but I sometimes use different tunings. I disagree about strumming in only one direction. I use both directions and sometimes finger-pick.
Sean mentioned a capo. With a guitar, you don't have to put any thought into the capo, since it is fretted chromatically, but a dulcimer, fretted diatonically, will change the relationship of the frets when you put a capo on it, so while it is possible to use a capo, it's usually not just to change the key. I first started using a capo thirty some odd years ago and at that time dulcimer capos were not available, so I used a chop-stick and an elastic band. I still prefer this capo for my dulcimer.
chopstick capo   
I also use a Bic pen lid with some modifications as a partial capo to capo just the bass string.
partial capo
The tuning I use is best for playing in G.
The G chord is 302 (GDB, treble to bass)
The D chord is 201 (F#DA) or partial D7 is 403 (ADC)
The C chord is 313 (GEC)

A good site is the Friends Of The Mountain Dulcimer