The DADGAD tuning is also known as Celtic tuning and hence often used for playing Celtic music on guitar. It can also be interested in lots of other styles if you like to experience.
Essentially, you tune to a Dsus4 chord (it is what you hear if you play all string open). Since the tones are close to many D chords, the tuning is extra suitable for playing in the D key.
The name says it all, but just to be extra clear, to get this alternate tuning you should tune your guitar according to this: D A D G A D.
Major and minor chords
The chords presented are in the key of D and most of them are movable. For example, 3332XX would be F major and 3331XX would be F minor.
You can choose to include the two highest strings or not. In most cases you get a more characteristic sound related to this tuning if you do.
If you have problem to get enough room for the fingers you could remove the finger from the 5th string and mute if with an adjacent finger.
The alternate D chord could also be played without the finger on the fourth string, in that case the correct chord name is D(no3).
More chords in EADGBD tuning
Other chords in this tuning:
Chord progressions with DADGAD tuning
Some examples of progressions using this alternate tuning:
D - Gadd2 - Add4 - D
Bm7 - Gadd2 - Add4 - D
Em7 - D - Gadd2 - Aad4
Em7 - F#madd - Gadd2 - D