The diatonic scale is the standard major scale consisting of whole and half steps, WWHWWWH (W= whole step H=half step).
The different modes just start on a different root note within that scale so it gives it a different feel, since the intervals are played differently (in a different order).
So Ionian (name of the mode) is the Major scale WWHWWWH and then a seperate mode of that scale would be Mixolydian (for example, there are 7 modes) which starts on the fifth note of Ionian and it looks like this:
WWHWWHW
see how that works it just shifts the root and there are the same amount of the same intervals just shifted over. Mixolydian is also a major scale because it doesn't have a flat third. There is a mode for every note (interval) in the scale.
This is covered very well in the theory section (there should be stickies for most of it in the theory forum). I could get into more detail but people who know a lot more than me have already written it so why waste the time.
Plus anyone feel free to correct me if I said something wrong, I am pretty sure I am right though.
There is a lot more too, but just memorizing those intervals is what you probably want to start with.
There is a great tutorial by ace on this I believe and a few other instructors have done similar tutorials all of which are great.
What i would recommend is finding someone very knowledgeable you can actually talk to. I think I would have gotten through this stuff much faster if I could have just kept bouncing questions off someone instead of having to read a bunch then go find a bunch more to read until I actually understood it.
The nature of music theory (at least in the beginning) seems to be every questioned answered leads to ten more questions.
It is also important though to not get too caught up in theory, it can help a lot but building an ear and just playing till it makes sense is more valuable in my opinion. Theory can help to bridge certain gaps until your playing and ear get to where you can just play and not think about it. I still use it all the time when composing and soloing.
