Open D Minor is simply a variation of Open D Major. The third string is lowered one tone from Open D, making it sound like a minor rather than a major.
D Major consists of D F# A, and D Minor consists of D F A, so all that needs to be done to get from Open to Open D minor is to drop that the F# to an F.
Like Open D, D minor is a very rich and resonant sounding tuning.
I suggest first tuning to Open D, then simply lower the 3rd string one step to an F.
| Strings | Standard | D A D F A D | Changes | Fret to Match Adjacent Open String |
| 6 | E | D | Lower 1 whole-step | 7 |
| 5 | A | A | - | 5 |
| 4 | D | D | - | 4 |
| 3 | G | F | Lower 1 whole-step | 3 |
| 2 | B | A | Lower 1 whole-step | 5 |
| 1 | E | D | Lower 1 whole-step | - |