Fretboard Map for Open D
Below is a map of all the notes of the D-major scale in the Open D tuning up to the 12th fret. Combined with the open strings, notice that there are three important hand positions on the fretboard for playing the majority of the notes; the second position, the fourth position and the ninth position. From these three positions you can move through the D-major scale without alot of hand movement.
If you're not familiar with the term position, this refers to where the index finger is positioned under the fretboard. For example, the "second position" would have the index finger of the left hand is positioned beneath the second fret.
From this map we can create scales at each key hand position. Then we can expand that to obtain scales that traverse up and down the neck. Once you've become familiar with these scales, improvising within a chord progression should become much easier. The goal of this tutorial is to equip you with enough knowledge to write your own music in these tunings.
The strings in these diagrams are arranged with the 1st string (highest frequency) on top and the 6th string (lowest frequency) on the bottom. To help guide you, the strings in the diagrams are thicker for the bass strings and get thinner as you move to the treble strings as they would be on a regular guitar.
Take a look at the notes at the 2nd fret: E B E G# B E. These are the notes for Open E tuning. If you were to tune your guitar to the Open E tuning, you would need to raise the tension on the 3rd, 4th, and 5th strings (G->G#, D->E, and A->B respectively). This is one of those tunings that adds additional stress to the neck and bridge of your guitar. Instead you may want to consider tuning your guitar to Open D and placing a capo at the 2nd fret. You get the Open E tuning without the stress!
Also, if you were to do a performance where you had pieces in both tunings, you wouldn't having to retune the guitar to move between them. A great way to break up the monotony of a set is to change keys. So the easier it is to change tunings during the performance, the better.
If you go through the tutorial section on Open G, you will see that you can also obtain the Open A tuning by placing a capo on the 2nd fret in that tuning. What is interesting in both of these cases is that you maintain the same note relationships and chord positions of the main tuning. Open E has the same scale and chord relationships as Open D, and Open A has the same scale and chord relationships as Open G. So by learning the chords and scales of two new tunings, you actually gain the ability to play in 4 tunings.