Is he tuner supposed to light up green when the string is correctly tuned?

Good question, tuners can be simple and some are complicated
a basic automatic guitar tuner you would not have to do anything to the settings, just tune normal on the E string then slowly down tune to D most tuners are a little sensitive, so go slow
and one thing I always do is go lower than the note I'm tuning to then tune up tell it's correct, strings seem to stay in tune better
Hope this helps ?
and if you have time check back on my profile
I will be doing some video tips this weekend
showing tuning, and some basic guitar repairs
thanks for your time

Actually, concert pitch is A=440 rather than A=400. Normally a 5 string banjo is tuned G (octave) D G B D though many variations exist.

Unfortunately, the manual on
http://www.korg.com/us/products/tuners/ga_40/

indicates that 12 string is not supported.

The owners manual can be downloaded at
http://i.korg.com/uploads/Support/GA40_EFG1_633661472559800000.pdf

The YouTube tutorial is at
https://www.youtube.com/watch?v=Of4CRajvq0E

with a 12 string, you can often tune the octave until the tuner sees the matching note. It won't see the correct string number, but an A note is an A note, whether or not it's an octave higher.

Hope that this helps.

Some tuners have a weird mode that one presses the button once and the tuner will pass the audio until it times out, then tuner and audio stop. Two presses kills audio while tuner works for a time period and then goes dead. A third press enables audio to pass for normal playing. These are confusing compared to other type built in tuners. If you have one of these read the CONFUSING instructions carefully...

Hi
Simply turn the tuner on using the power button. Play an open string note close to the tuner (no more than about 1/2 metre away) - for instance the low E on string 6.
The built in microphone will pick up the sound and, if your guitar is reasonably close to being in tune the led light labelled 'E' will illuminate on the lower scale on the tuner along with one of the three other leds to indicate whether the note is flat (b), in tune (green) or sharp (#).
Due to harmonics any or all of these three leds may flash but it is the one that is on the most that matters.
Adjust the tuning peg until the green is on constantly when you play the string.
Move on to the next string
Note - if the string is more than a semitone sharp or flat a different light may flash (e.g if the low E string is 3/4 of a tone flat the D light will come on).
If you wish to tune your guitar to another instrument that is not at perfect pitch (and perhaps cannot be easily adjusted - like a pipe organ) you can use the calibrate button to adjust the setting of the tuner. This temporary recalibration will be lost when the tuner is turned off.

Are you sure you are struming the G string at the right point? One might be able to fool the tuner by triggering a harmonic on the strings or being too aggressive in the strum.

I would pull the peg and see if the string CAN be tuned manually. It is possible the G string is bad or somebody put the wrong string on there.

Remember that strings can be within about 10% of the breaking tension when in tune.

Also it appears that the thing can detune itself to nearby keys. Make sure you have the dial set correct when you pull it out to tune.

well i hope you've figured it out by now, it's a really cool looking tuner and i love it. but if you are still having problems...
the switch on the left side: OFF, ON, LMP (ON with a little light so you can see in the dark)
The number and letters you see across the top of the interface indicate which string it is tuning to. 6E is the low E string (the thickest one) and 1E is the high E string (the thin one on the bottom of the guitar), i've seen many people get confused when they've tuned those two.
You can leave the tuner in auto and it will pick up what string you are trying to tune. but if you are having problems getting the correct string or whatever the case is, you can switch to manual mode. click the only button on the tuner and the specific string will light up on the interface.
If you press and hold the button, the tuner will go into flat mode, tuning all the strings flat.
once you have the right string and you're tuning it in, you want the needle to be centered.
that's pretty much it. enjoy!

That's the problem; you're using light gauge guitar strings. Chances are that if you are not used to playing strings that light, you're fretting hand will hit the strings with more force than is neccesary to fret them, thereby forcing them out of tune. You can solve this problem by adding more winds around the string post (three or more winds should do it), or you can switch to a heavier gauge of string.

If they're true locking tuners, they should have a notch on the back of the gear housing that you turn with a nickel to engage the locking mechanism once tuning has been established.

Also; check the intonation of the guitar itself on an electronic tuner. If it tunes right but sounds out of tune when played, this is an intonation issue, and can be solved by adjusting a small set screw that moves the individual saddle back and forth in the tune-o-matic style bridge. You can check this by tuning the string to the correct note, then playing the same string at the 12th fret and checking it against your tuner. If it rings in true, you're fine, if it comes up flat or sharp, every note on the fretboard is going to be off by that much, and you'll have to adjust accordingly (turn the screw to the right to add length and lower a sharp note, turn the screw to the left to subtract length and raise a flat note, if I remember right).

Hope that helps.

i don't really know what instructions you expected, although you should have received something for the tuner and amp. I suspect that you are new to playing the guitar, as, I don't wish to sound disrespectful, you would know what to do! So first, and again I hope not to sound like I'm treating you like a dummy, plug the guitar into the tuner input. Or if It's a piezo tuner clamp it to your headstock. Most tuners are now automatic so it should pick up on the string you are striking.Repeatedly pluck the same string til the tuner changes colour, or flashes, or some other indication to tell you the string is at pitch. Repeat the above for all 6 strings.
Then plug the cable into the amp input, switch it on, and bugger about with the controls til you get a half decent sound. ( thats what the rest of us do).Don't expext too much from this package, it is budget level, but of quite good overall quality.hope this helps