Any readers may thank you more if the new key becomes Ab.
Ab has only 4 flats in it, whereas G# has 8 sharps.
The simplest, which always works, pretty well whichever key you're changing into, is to use the dominant of the new key for a bar.
Thus Eb or Eb7 will do the trick.
I've done it hundreds of times with choirs and bands and soloists - some of whom were genuinely unaware that a key change had actually occurred!
It works really well when going up a semitone, as there are common notes involved.
Think G - G B D, and the V of
Ab - Eb G
Bb Db. O.k., just the one!
but all the others are only a semitone from notes of G. Then Eb7 leads almost automatically to Ab. Going to any other key, ii-V-I is a tried and tested move (in the new key!)
music.stackexchange.com/users/2808/Tim
Just jumping up the key up a semitone without a chord progression to lead into the modulation is a very common musical trope!
Simply change the key signature in-between two major sections of a song, such as transitioning from a verse to the chorus - the already-present transition prevents the sudden modulation from sounding out of place or overly abrupt.
This is sometimes called the " truck driver's gear change " and shows up frequently in pop, rock, and dance music.
When you abruptly modulate up a semitone, it immediately adds a lot of energy to a song.
As a result, it's most frequently used at the start of the final chorus of a song to make the ending have more of a punch to it.
I Won't Let You Down by OK Go has an excellent example of this modulation near the end of the song .
Run and Gun , an electronic dance track, starts with this modulation to gain some surprising energy coming out of the intro into the first drop.
The truck driver's gear change is somewhat cliche and, to my knowledge, rarely shows up in academic, classical, or neoclassical music, so it may not be an appropriate tool for the style of music you're writing.
music.stackexchange.com/users/3265/Kevin
A little more advanced method is to look at the shared notes between the two scales you're trying to modulate between (using enharmonic spelling to keep things simple):
G maj:
G A B C D E F#
G# maj: G# A# C C# D# F G
So the only shared notes are C and G.
Now make lists of all the run-of-the-mill triads you can make using those two notes in each of your two keys:
G major: CDG (Csus2),
CEG (Cmaj), CFG (Csus4)
G# major: CD#G(Cmin), CFG (Csus4)
Now look for any shared chords between the two keys.
There's only one in this case: CFG (Csus4).
That will be your most important one to modulate between the two keys, the 'pivot'.
From here, it's just a matter of playing around with those chords above until you find a progression you like.
For example, I came up with this one that sounds nice after a bit of noodling that lands you in G#maj: Csus2, Cmaj, Csus4, G#maj Edit
: Found these interesting plays on the I V vi IV progression that start in Gmaj and end in G#maj: Gmaj, Dmaj, Emin, Fsus4, G#maj, D#maj, Fmin, C#maj
If you sub Fmin->Fmaj you get a very interesting chromatic cadence with some delicious harmonic ambiguity: Gmaj, Dmaj, Emin, Fsus4, G#maj, D#maj, F maj , C#maj
music.stackexchange.com/users/28028/Eriek
One option is to take a detour through F# major.
We use a trick of borrowing the minor subdominant from F# to get us to the subdominant of Ab.
Then you've got a nice sounding IV-V(7)-I and only one minor chord which can easily be paved over when voicing it out: G Bm C#/Db Eb(7)
Ab G: I iii
F#: iv
V
Ab: IV V(7) I
music.stackexchange.com/users/20714/Sabre
Perhaps not what you are looking for, but I recall "Sampo" (Stroll) from Joe Hisaishi (opening theme of "My neighbour Totoro") which in the reprise repeats the full song a semitone up.
In this guitar arrangement of mine , you can see (and hear) the simple modulation: from the concluding chord (tonic) of A major, with higher note A, the chord is suddenly replaced by F7, (keeping the A high note)
- this is the dominant of Bb, which turns to be the new tonic.
music.stackexchange.com/users/460/leonbloy
Try G-major chord, followed by B-major chord (raising the iii-chord in key of G up to a Major), then follow with C#-major and then D#-major, which are the new IV and V chords of the new (raised) Key of G#.I'm still trying to find the theory-reason why the B-major works, but I've played it multiple times and it sounds to the ear like it "works.
"David : )
music.stackexchange.com/users/70513/David Johnson
With most modulation there is a balance of technique (harmonically) and dynamics.
I won't pretend to know very many common harmonic sequences that will get you a half step up, but if you lack the technique, you can always set your audience up for a would be jarring transition by slowing down, and lowering to volume, then coming back to speed and volume after a simple chromatic step up.
The augmented fifth is always an interesting sound, and could be a nice hint for your listeners.
music.stackexchange.com/users/41362/user7778287
I was asked to incorporate a modulation that goes one semitone up in a song initially written in G. So at some point it should go from G to G#.  I am having a lot of trouble finding a relatively nice sounding chords to transition smoothly from G to G#. Is there some known trick or commonly used chord(s) that makes this modulation flow nicely ?
modulating from G major to G# major
music.stackexchange.com
<chords><chord-progressions><modulation>
music.stackexchange.com/questions/58750
music.stackexchange.com/users/30493/Joulin Nicolas
With most modulation  there is a balance of technique (harmonically) and dynamics.  if you lack the technique to make the modulation, you can always set your audience up for a would be jarring transition by slowing down, and lowering to volume, then coming back to speed and volume after a simple chromatic step up. The augmented fifth is always an interesting sound, and could be a nice hint for your listeners.  The augmented fifth is always an interesting sound, and could be a nice hint for your listeners. 
Harmonically there is a balance of technique (harmonically) and dynamics. The augmented fifth is always an interesting sound, and could be a nice hint for your listeners. If you lack the technique, you can always set your audience up for a would be jarring transition by slowing down, and lowering to volume.