The Dorian Mode

The Dorian mode starts on the second scale degree and like the corresponding chord is minor in nature.  It can help give a jazzy feel to your music, without necessarily having to learn loads of jazz theory.
In the Key of C :  C D E F G A B C  the second scale degree is D so we have a D Dorian in this Key.
D Dorian:   D E F G A B C D    The intervals are therefore T S T T T S T
If we compare to D Major : D E F# G A B C# D  we can see that the Dorian mode has a b3 and b7 compared to the corresponding major scale.
An example pattern starting on the A string is shown below.  I’ve started on the A string to keep the fingering pattern fairly uniform.  As with the major scale example, you definitely want to experiment a lot with playing this pattern in as many different positions as possible:
D Dorian-page-0
If you need a diagram showing the notes on the fretboard, one is available in the Ionian mode (Major scale) post.
How you play these modes is really up to you.  You could use a Dorian mode all of the time as it will fit with any chord in the key.  For variety you can mix them around a bit, often minor modes will be used over minor chords and major modes will be used over major chords.  The best thing is to experiment with voicings and phrasings to find the sort of sounds that you like.
As an example to get you started, I’ve created a simple C Bm F G (I vi IV V) chord progression which repeats four times and has the Dorian mode played over the top of it.  The tab can be downloaded from here  Dorian example  (note the chords are not shown on the tab but there is one chord per bar) and the audio can be downloaded here 

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