Is there an established way to choose what mode/key to modulate to from the mode the composer is currently using?
Modulating from C major to F major or G major, for instance, is "easy" because there are a lot of chords in common. Would the same apply for modes, e.g. use modes that have a lot of common tones/chords?
It really depends on what you're trying to achieve. If you want the modulation to be sudden and jarring, then you might choose to modulate to a key area (or new mode) with minimal common tones.
But if you're simply going for ease of modulation, then yes: by and large, the easiest modulations are effected with two key areas (or modes) that share the most common tones.
If you're in F Lydian, for instance, you could modulation to A Dorian pretty easily since you're only adding a single sharp.
With that said, in my experience it's easier for students to modulate when there is at least one new accidental. Modulations where there are no new pitches (like F Lydian to G Mixolydian) can often be really tricky to write effectively.
Lastly, this rule—that more common tones makes it an easier modulation—has one main caveat. The so-called "truck driver modulation," that just moves up or down by half or whole step, is very easy to do without any preparation at all. You just move transpose the music into the new key; it's really as simple as that. It's a little jarring, but it's so popular (dare I say overused...) these days that it no longer sounds surprising to us.
Don't modulate because it's 'easy'. Modulate because it takes you somewhere you want to go.
Sometimes there's a NEED to modulate, perhaps to accommodate vocal range. Here's a wonderfully ingenious example of sounding as if you've done a 'truck driver' up into the last chorus but actually ending up a semitone LOWER to the rest of the song!
Here's another particularly nice modulation, recently quoted in another forum (from 'Pippin'). It's largely melody-driven. The bass note moves by a third - often a feature of an 'interesting' modulation. (A favourite device of 'The Great American Songbook' was to modulate up a minor 3rd, C to Eb.)
You'll notice that I'm offering you examples, not rules. These were from my favourite musical world. Look at the repertoire of yours and see what composers HAVE done that you liked.
In pop songs what is common is to modulate a note higher in the climax, for example if you are in C maj you modulate to D maj, in a lot of songs its also common to modulate to the relative minor key, but in the end i think it justs depends on whats your plan for your piece, and acording to that you modulate or not, theres not given rule in creative practice
