Usually a song's key will be found with the chord that seems to 'attract' every other note. That chord is usually the root (or first note) of the scale used in the tune.

If you play a chord scale, you get (in G major)
G Am Bm C D Em F#mb5
That's pretty close to what you have, right? The last chord is pretty weird, it's not really used in pop or rock. Your progression is in G. The F can be explained by many different chord substitution, too long to explain right now.

Anyway, in Major, you always have that kind of progression
I IIm IIIm IV V VIm VIImb5

And in Minor, you start with the 6th note

Im IImb5 III IVm Vm VI VII

That's the basis for modes too! The first is a Ionian progression, and the second an Aeolian one.