Singing will help get the sound but you want to have something playing the related chord. So if playing Dorian you want a Mi7 chord playing. Then do your analysis and look for the notes that differ from major or minor. So back to Dorian compare to a natural minor scale and see the major 6 in a minor scale is the difference. Now back to playing the mode and listen to the sound of that major 6 against a minor chord. Do this with all the modes, by the time you do that you do all that you should have the fingering down, know the related chord, know the note(s) that give the mode its sound, and have experiments making music or soloing with it.
Now here is a routine a teacher I had used.
1. Play the scale/mode over two octaves (or more.)
2. Play the related arpeggio up to the 13th over two octaves.
3. Play a pattern using that scale (3rd, 4ths, sequence). Yup over two octaves.
4. Now sit and improvise using the scale/mode.
Do this on one scale/mode over a chord in a key. Do this for about 10-15 minutes a day for a week. Then move to another scale/mode chord or key the next week. Do this short routine and you will master your scales/modes, develop your ear, build fretboard knowledge, and how to use musically. If into Jazz this process will take a couple years to finish because their are around 100 chords and related scales/modes to work on (basic chords X 12 keys).
Okay timer set for 15 minutes, now get to work.
