Heres an exercise that I use a lot either when warming up, teaching or trying to learn new modes.
If we take the major modes...
Starting on, say, G.
G - Ionian
A - Dorian
B - Phyrigian
C - Lydian
D - Mixolydian
E - aeolian
F* - Locrian
The exercise involves playing each interval of the scale on by one in each mode.
Play the root of each mode on the E string (going up one string punk rock style), followed by whatever interval your on.
So if we start with 3rd's we get a tab that looks something like this....
A----B---C---D---E---F*---G---A
E--G---A---B---C---D---E---F*--
So what we've done is play the root of each major mode in G followed by its 3rd.
See that Ionian, Lydian and mixolydian have major 3's while Dorian, phyrigian, Aeloian and Locrian have minor 3's
Then we progress to 4th's. so...
A----C---D---E---F*---G---A---B
E--G---A---B---C---D---E---F*---
This time we notice that all the modes have perfect 4ths, except lydian which has a sharp 4.
Notice that throughout this exercise we never play a note outside of the G major scale.
5ths,
A----D---E---F*---G---A---B---C
E--G---A---B---C---D---E---F*---
This time we see that Locrian has a flattened 5th, while all others are perfect.
6ths
D----E---F*---G---A---B---C---D
A-----------------------------------
E--G---A---B---C---D---E---F*---
This time we see that Ionian, Dorian, Lydian and Mixolydian have major 6th's while Phyrigian, Aeolian and Lociran have minor 6ths.
7ths
D----F*---G---A---B---C---D---E-
A-----------------------------------
E--G---A---B---C---D---E---F*---
Ionian and Lydian have major 7th's, while the rest have flattened 7ths.
9ths (For me 9ths are better to learn than seconds. Partly for the techinque building, partly because 2nds would be hard to hear but mainly because 9ths are more commonly played than 2nds)
G----A---B---C---D---E---F*---G
D----------------------------------
A----------------------------------
E--G---A---B---C---D---E---F*--
with 9ths/2nds we see that Locrian and phyrigian are the exceptions with flattened 9th's/2nds
I'd extened the exercise to 10ths (3rds), 11ths(4ths) and 13ths (6's) as well.
This exercise allows you to see how the modes are constructed 1 interval at a time. As you are playing the intervals at the same time then you are able to
1. hear the differences
2. Get those intervals under your fingers
3. realise that the major modes all use the same notes as each other but by shifting the root you get a totally different set of sounds as the importance of each note changes.
Hope this is of some help in getting modes under your fingers.