Making Chords from the Major Scale
A little on chords themselves: a major chord is made up of three notes, 1st 3rd 5th (from it's major scale). A minor chord changes slightly and is made up of 1st b3rd 5th (the 3rd is dropped by a fret). You can see this in any given open chord major and minor pairing.
That being the case, we can turn the notes of the major scale into full chords by taking each degree and finding its relative 3rd and 5th. Following that process we get:
1st - Major
2nd - Minor
3rd - Minor
4th - Major
5th - Major
6th - Minor
7th - Diminished
Therefore if we took the G Major Scale, the chords in the key of G Major would be: G Am Bm C D Em F#dim.
Just like in the scale, these chords would naturally resolve to the root (G).
Some common major keys in songs: E, G, C, A, D
Here are some progressions from popular songs, the key they're in, and the chords of the key used.
Perfect - Ed Sheeran (G)
Verse - G Em C D (I vi IV V)
Chorus - Em C G D (vi IV I V)
Blank Space - Taylor Swift (D)
Verse - D Bm G A (I vi IV V)
Chorus - D Bm Em G (I vi ii IV)
Sign of the Times - Harry Styles (F)
Verse and Chorus - F Dm C (I vi V)
Bridge - F Dm C Bb (I vi V IV)