5.2 The D Major Chord video
Tunefox Mandolin Lesson #5
The D major chord is a different shape than your G and C chords, but it still only uses two fingers.
Starting with your C chord, move your index finger to the 2nd fret, 4th string. Now take your middle finger and move it to the 2nd fret, 1st string. Your 2nd and 3rd strings should be open. Make sure you're both pressing down enough to hear the fretted notes and you are arching those fingers enough so they aren't touching and muting the open strings.
The D Major Chord Mandolin video lesson
Strum with downstrokes to start out and then alternate between down and upstrokes.