Most simples rules:
1. Watch out for major-chords in fifth-distance to each other. The harmonically lower one of both may be the key-indicating tonic.
2. Watch out for major-chords with an added minor-seventh, e.g. G7, B7. If you find such one, then the chord (major or minor) one fifth below may be the key-indicating tonic, e.g. C or cm according to G7; E or em according to B7.
3. Verify the result of the rule by ear: the key-indicating chord is the one on which you would most likely let the song end, if you had to decide yourself.
For other rules, e.g. for songs in minor keys, see the explanations below.
In his post Russell Harding may have used some knowledge about harmony theory. I suppose he recognized that there is a chord in major with a minor-seventh and according to this chord the (major) chord one fifth below:
D7 --------------------------------------------- G
Dominant-7 ------------------------------------Tonic
V7 ----------------------------------------------I
The minor-seventh on any major-chord makes this very chord a dominant in each case, what in turn determines the key. (This is in fact an application of harmony theory.) It may be even in some way independent of the key signature.
You need the couple of
X(7) --------------------------- "X-minus-4" (major chord one fifth below)
or in numbers:
V(7) ----------------------------I
Here X-minus-4-major is the key.
In some cases the key may be minor:
X(7) --------------------------- "x-minus-4" (one fifth below, but minor)
V(7)---------------------------- i
In other cases the dominant may be minor too:
x --------------------------- "x-minus-4" (one fifth below)
v-----------------------------i
And then there may be cases where the dominant is replaced by it's related minor chord:
iii ------------------------- I
e.g.
em ------------------------C
If the results of these rules are not satisfying, you may look look after three major-chords in the distance of fourth and fifth.
For example: G- C- D ... in which case the key is likely to be the G.
To make it even more complicated: some of these three might again be replaced by the related minor ones:
G- am - D
G - am - bm
In turn in minor for example the Dominant may be replaced by its related major chord (for which as an example "Working Class Hero" with em-D-em comes to my mind)
VII ---------- i
G ---- am instead of
E or em --------am
In Lady d'Arbanville you find both bm and its substitute D according to the tonic Em and you can compare what each of them does. In Sister Morphine you find several such substitutions: C G F Am while the song proclaims to be in am so that either the song should rather be in C or the three major chords are substitutes. (Don' think too much about the change Dsus2 - Am in Sister Morphine. Maybe it is just a colouring of the am ...)
But then there are songs that work differently, even some extremely popular ones. Yesterday I played Mack the Knife with my son and had the impression that it is one of those which essentially swing around between tonic (I) and subdominant (IV, here replaced by its related minor ii) with the dominant in no substantial role (and the song even being possible with this one left out). In these cases I would construe the last chord of the melody line as the tonic, even though one wouldn't find any distance of a fifth at all. (But this could only be the case if there were no major chord with seventh at all).
To explain this strange behavior: It may be the case that the melody itself would be harmonically significant enough to undertake the task if indicating the tonic, so that the chords may create tension by staying away from it. In such a case a sheet with lyrics and chords alone may not suffice to determine the key, as long as you haven't got the tune in mind.
In the end it still helps to "feel" where your home is. This can be tricky either. "If I were a carpenter" for example has D - C- G and you may feel the center at D which is the V according to the rules mentioned above.
(These rules are the ones that work best for rock and folk. In jazz the dominant has further subtitutes.)
