Minofmusic is right. D dorian is born out of C major or you can say the relative major of D dorian is C major. Therefore you can use the same key signature of C Major (Ionian) and D dorian. Otherwords No sharps or no flats. Dorian mode is located on the 2nd step through the 9th step or degree of any major scale. The 9th degree of the major scale will be the octave of the 2nd degree. Example.
C, D, E, F, G, A, B, C, D
1, 2, 3, 4, 5, 6, 7, 8, 9
D TO D, but keep playing C major but start on the 2nd degree of it and end up on the 9th of the C major scale and you will hear dorian. By starting on the 2nd degree, the half steps will shift for dorian automatically.
D, E, F, G, A, B, C, D now lets renumber dorian so it will show half steps for dorian between 2 & 3 (E,F) and 6 & 7 (B,C)
1, 2, 3, 4, 5, 6, 7, 8
Notice half steps for the major scale is between 3 & 4 and 7 & 8 (Still E,F and B,C) same notes but different degrees since they are renumbered or start differently.
You will get it.
G dorian is born a whole step back out of F major
E dorian is born a whole step back out of D major
A dorian is born a whole step back out of G major
B dorian is born a whole step back out of A major
C dorian is born a whole step back out of Bb Major
D dorian is born a whole step back out of C Major
F Dorian is born a whole step back out of Eb Major
Etcetera
Good Luck!