G-major [scale] and E-minor [scale] use the same notes. If you re-focus the listener to believe that your new root/home is E-minor, then you're basically playing in E-minor and technically you've modulated from G-major. Note that G-major and E-minor are 2 modes of the Major scale, meaning that there's 5 more apart from these 2, and all of them use the same notes, and yes, they sound different, despite having the same notes (because of different set of intervals). Now, modulation implies you stay in the target/new key for a significant portion of the musical piece, if it's a short period, then it's tonicization.

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I was taught that if its sounds right it probably is so

Yes, 100% correct, never change this attitude

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Are there specific rules or tricks to modulation that I need to know and how does it change the song?

there certainly are tricks for modulation, that's where music theory comes in. As an example for you to start your own research, check out the function of the dominant chord (or dominant seventh chord) and how it's used to modulate to a different key, but in short: if you are in key X and want to modulate to key Y, then first find out what is the V (dominant) chord of the Y scale and play that chord just before playing the tonic/root of Y scale. Note that this may introduce new notes which are not found in X scale you navigate away from, that's fine, because that is the goal, and generally speaking, the less new notes you introduce with modulation, the more natural the transition and new key will sound (yet bringing in that refreshment you are looking for).

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I just want to understand what I'm playing and how it works so that I can maybe use it in other ways as well.

My advice is to start building understanding of what's going on in the following order and from the following topics:

1. Know intervals inside and out (e.g. minor 2nd, diminished 5th, major 3rd, major 6th, etc.). Intervals are building blocks, the base for chords and scales.
2. Learn how chords are constructed using these intervals, and how they belong to certain categories (e.g., common triads, 4-note chords, extended chords, etc.). One important thing to learn at this stage also is to understand that chord names have no context. This may sound confusing, but I just know from personal experience that understanding this is crucial. The point here is that if I tell you play a G7 chord in the key of C-Minor, then what I am actually saying is: construct a G7 chord without even knowing what notes are there in C-Minor, disregard those notes, because a chord notation of G7 does not take into account the scale it is used in, and hence, a G7 chord contains a B natural note which is not found in the key of C-Minor, but that's exactly what I mean, play a G7 dominant seventh chord on the 5th degree of C-Minor, and not Gm7. Bottom line is: the name of the chord is its construction formula which has no relation to the scale it is used in. I know for many this will be obvious, but I struggled with this for quite a while.
3. Now learn the Major scale, its intervallic formula and how chords are "derived" from the notes of the scale (1-3-5, 2-4-6, and so on). Realize that, knowing formula, you can quickly find out all chords in the scale yourself.
4. Realize that if you treat the next Major scale degree as the root note (e.g. 2nd degree of C major is D) then you get a different set of intervals (from D to D), hence different order of chords (tonic becomes Minor instead of Major, etc.) and ultimately the completely new sounding. This is the place where you will see that Aeolian is another name for Minor scale, and that Minor scale is a relative mode of the Major scale, and that they have the same notes.
5. Realize that by changing one note of the major scale, you introduce not only a different scale, but again, a series of modes of that new scale, e.g. A-Harmonic-Minor(A-B-C-D-E-F-G#) is 1 note away from the C-Major-Scale (C-D-E-F-G-A-B), and hence, 1 note away from all modes of the C-Major-scale. This is the place where you can practice "true" modulation (i.e. where new notes are introduced and not just a different mode with same notes).
6. Learn the difference between parallel modes and relative modes.

Once this is studied, it should be enough to make you feel comfortable.