Feeling kind of crappy today so not sure how in depth I'll go with this but the easiest way (IMO) to understand modal theory is on a piano keyboard.
Find a C (white key next to the series of keys that have two, not three black keys). Play all the white keys (no black keys) up to the next C (one octave higher). This is of course the C major scale. Look at where the unplayed black keys are positioned. It will create the tone/semi-tone pattern of the Major scale which in modal theory is called the Ionian mode. Now move up one white key (which is D) and play all the white keys up to the next D. That is the Dorian mode and again the black keys will show you the Tone/Semi-tone patter of Dorian. Just keep moving up one white key at a time until your starting point is on C again (an octave higher than where you started of course).
These are the "natural" modes of C Major. The capitlization (or lack thereof) of the Roman numerals denote the "quality" of the triad chord created by the mode (capitalized = Major triad, not capitalized = minor triad*):
I = C = Ionian (Major scale)
ii = D = Dorian
iii = E = Phrygian
IV = F = Lydian
V = G = Mixolydian
vi = A = Aeolian (natural minor)
vii* = B = Locrian (please note that Locrian has a diminished 5th, the only natural mode that does, and is sometimes referred to as a half diminished scale)
You can train your ear to recognize the feel of each mode through sequential repetition which become important when applying modes to other keys.
To translate this to other keys just find/pick a root Major for whatever key you want to play in. Using the Circle of Fifths to work through all the keys and their modes sequentially is extremely beneficial and how I learned to play all modes in all keys in all positions.
So take that Root note and play your Major (Ionian) scale to see where the sharp and/or flat notes appear. For example moving one step up in the Circle of Fifths will land you on G which has one sharp note that appears on the 7th step. That will remain the only sharp throughout all of the modes of G Major so you can just do what we did before and move up one note at a time playing up to the octave.
You may be familiar with the conept of "Relative Major/minor" in more traditional theory. They use the same notes but at different starting points. Modal theory just fills in the extra five scales within the keys.
HOWEVER be aware that Harmonic and Melodic minor do NOT fit in to any of the natural modes (this is why Aeolian is referred to as the Natural minor). For both of those scales you are slightly altering the natural pattern. In the case of Harmonic minor you raise the 7th step of the Aeolian mode one semitone. This will create an entirely new set of 7 modes you can play with (and some of them are pretty freaky deaky).
For melodic minor (and my addled mind is hopefully not fudging this up) you take the pattern of a Major (Ionian) scale and flat the Major 3rd which makes the scale minor. HOWEVER it's position in the modal steps is still on the vi (sixth) step of the relative major scale. Again this creates a whole new set of modes to play with.
There are many different names used in different genres/theories for these altered modes but to make things easy on myself and others I just name them after their corresponing natural mode and add Harm or Mel in front.
So "Harmonic" Aeolian or "Melodic Lydian".
Also note that in traditional classical theory you only temporarily shift to the Harmonic/Melodic minors at specific times (I don't think I want to dig into that too much right now because it requires some extra mental trickery) whilst generally playing in the natural modes/chords. With melodic minor in classical theory there is another weird thing where it's played different going up than it is going down (don't even get me started how weird and dumb that is but it's what they do). IIRC the upward version of Mel minor is the altered variant (so actually melodic minor) and then on the way down it's played as natural minor (Aeolian). I may have that flip flopped in my head though.... rough night.
So you've essentially got 7 modes x 3 for a total of 21 distinct diatonic modes.
If you work through it all methodically and in every key (using the CoF) then you can pretty much do anything. Most other scales are just variations based on those modes that drop a couple notes (like pentatonic scales) or add in chromatics at specific spots (like the minor blues scale or mixo blues scales).
The only other commonly used scales NOT covered by this theory are symmetrical scales but they are pretty simple to figure out.
Hopefully that helps you (and I didn't miss the point), Starise.
Cheers!