The most commonly used tunings today are DAd and DAc (reading from furthest, bass, string, to nearest, melody, string). They are versatile and straightforward, with decent sounding relative chords (C and G) readily to hand. They give you the normal D major and D minor scales, starting on the open melody string and 1st fret respectively, but both require a 6+ fret (between the 6th fret proper and the 7th, octave fret) to complete the scale. These tunings work well with modern chord/melody playing, where each string is used to play a different note and the melodies mainly use conventional scales.
Older instruments may not have the extra fret, nor will their fretting pattern or bridge position necessarily work happily with these tunings. For them, DAA or DAG are the equivalents, with the D scale starting on the 3rd (major) and 4th (minor) frets respectively. Although chord/melody playing is perfectly possible, these tunings are more often used where the melody line of the music is played almost entirely on the melody string – noter/drone playing for example. The drone effect is strong in these tunings and melodies using modal scales sound very much at home.
Less well used – unfairly – are three other tunings: DGd, DF#A and Ddd. DGd, with the scale starting at the 3rd fret of the melody string, puts you in the key of G. Immediately, you can play along with many of the UK session tunes, French dance tunes, old time and bluegrass music etc. Again, it’s versatile, straightforward to chord and is particularly suited to flatpicking. DF#A, or 1:3:5 tuning as it is often known, is unique in being a chromatic tuning – i.e. somewhere across all three strings you can find every note you need, including all sharps and flats. Yes, you will have to work harder, but you can produce more varied “colour” chords and play music which modulates between different keys or has chromatic runs. For more information, try this site http://www.mountaindulcimer-1-3-5.com/ . Ddd is almost the polar opposite, being a simple drone tuning and thus often called bagpipe tuning. Yet it also has a degree of versatility, because it allows you to play in D and G simply by starting at a different place on the melody string. It is also used on a particular type of big, elliptical dulcimer, often played in small string bands alongside fiddles and banjos – needing therefore to be loud and play in D and G. This type of dulcimer was made originally in the Galax region of Virginia, hence the alternative name for unison/bagpipe tuning – Galax tuning.
A dulcimer capo gives you further options, but you really need a 6+ fret to make this work best for you. With the capo on the first fret in DAD, you are actually tuned to EBE and in the key of E minor; or in DGD tuned to EAE in the key of A minor. Capo the 4th fret in DAD and you are tuned to AEA, in the key of A minor OR A major, with a useful 1+ fret; in DGD, tuned to ADA in D minor or D major, again with a 1+ fret.
Of course, this discussion assumes that you share the modern obsession with accurate tuning to a precise note. In the old days, a dulcimer player might well have tuned his melody string to an acceptable tension for playing, or perhaps pitch for singing, then tuned the other two unfretted strings to make a pleasant chord behind it. So early recorded tunes were as likely to be in C or E as D.