You have the right foundation to start experimenting with modes.
At risk of more intimidation, think of it as follows:
Major scale = Ionian mode.
You want mixolydian? Just lower the 7th. And adapt any chords accordingly.
E.g., if you're in key of A major (which may use chords D, E(7), F#m, Bm, C#m), lower the G# to G. That gets rid of your E and C#m chords. Use Em and G instead (forget about C#dim, you don't want that!).
Just remember
you're not in the key of D major. It's all the same notes and chords, but
A is your key chord and key centre.
You will find this an extremely familiar sound. Mixolydian is probably a more common sound in rock music than the major scale.
BTW, don't be tempted to solo in A minor pent. That just turns it in
Blues 
. Use A major pent, and add D (4th) and G (b7).
The simple version is just an A7 chord, while you improvise over it using the D major scale (A as root note, listening for the effect of the C# and G).
Minor scale = aeolian mode.
You want dorian? Just raise the 6th, and adapt any chords accordingly.
E.g., in the key of A minor, you have the chords Am, Dm, E (yes), C, F, G. Maybe Bm7b5 or G#dim7 if you're getting jazzy (but I'm guessing not...
) E major (or E7) is a harmonic minor chord, so lose that. And Dm will be replaced with D (or D7), and you can now have Bm(7) in place of that jazzy Bm7b5. You can use Em, which belongs to both A aeolian and A dorian.
Again, this is a really common sound in rock. You'll have heard Am7-D7 (back and forth) countless times.
You
can solo in A minor pentatonic here, but be sure to add the B (2nd) and F# (6th) for the full dorian effect.
The simple version is just an Am7, while you solo over it using the G major scale (A as root, listening for the effect of the B and F#).