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The simplest type of chords are triads, which are composed of three notes. There are only four types of triad.
Two of them are extremely important and common and are the familiar major and minor chords.
The formulae for those chords are:

Major = 1 3 & 5
Minor = 1 b3 & 5

The major chord
Both are in relation to the major scale. But which major scale? The one that starts on the chord’s root. So if we want to know the notes of the chord C major, for example, we take notes 1, 3 & 5 of the C major scale. The notes of the C major scale are CDEFGAB and notes 1, 3 and 5 are C E & G.

That means that the chord of C major contains those three note names and no others. It can have duplicates, though. On a six string guitar, it can have maybe three Cs an E and a couple of Gs – or any other combination. A pianist can manage up to ten using every finger – but still must play only Cs Es and Gs. At the risk of labouring the point, a full symphony orchestra can have well over seventy notes in a C major chord – but every one, without exception, will either be a C an E or a G. As long as it has no notes other than those it is a C major chord. If you add any note other than C, E or G, it will no longer be a C major chord.

Here are some common C major shapes using the string/ frets notation with the equivalent notes contained in the chord. (X = unplayed string)
X 3 2 0 1 0 = CEGCE
0 3 2 0 1 0 = ECEGCE
3 3 2 0 1 0 = GCEGCE
X 3 2 0 1 3 = CEGCG
X 3 5 5 5 3 = CGCEG
8 10 10 9 8 8 = CGCEGC

The minor chord
The formula of the minor chord is 1 b3 5. Again we use the notes of the major scale. To find the notes of the chord, C minor, we use the C major scale. (CDEFGABC).

The first note is C, exactly as it was with the C major chord.
Next we want the note flat 3 (b3). C major's '3rd', as we saw, is E. To make it a flat third (b3) we simply keep the letter name but lower the note by a semitone (or half step) i,e., Eb, instead of E.
The next note is note 5 of the scale, which is G.
So the three notes of our C minor chord are C Eb & G. compared to the C major chord which are C E & G
Comparing them side by side we can see how they are closely related.
C major = 1 3 5 = C E G
C minor = 1 b3 5 = C Eb G

Here are the two most common C minor shapes
X 3 5 5 4 3 = C G C Eb G
8 10 10 8 8 8 - = C G C Eb G C

Other triads
Two other triads exist, though they occur much less frequently. They are the diminished and augmented chords and consist of the notes
Diminished = 1 b3 b5.
Built on the root note of C, we would have C Eb and Gb.
Augmented = 1 3 #5.
Similarly a C augmented chord is C E G#

Diminished chords are often represented by the symbol, °
Augmented chords are often represented by the symbol, +

Summary of triads
C major = 1 3 5 = C E G
C minor = 1 b3 5 = C Eb G
C diminished = 1 b3 b5 = C Eb Gb
C augmented = 1 3 #5 = C E G#

Triads: chords built from thirds.

If you're familiar with intervals, you can also think of triads as stacked thirds, i.e., intervals of thirds built on top of other thirds, as follows:
Major chord = Maj 3rd + minor 3rd
Minor chord = Minor 3rd + major 3rd
Augmented chord = Major 3rd + major 3rd
Diminished chord = Minor 3rd + minor 3rd.

PRACTICE SECTION
Follow this 3-step method to produce any major, minor, diminished or augmented chord.

Example
Make the chord G minor

Step 1 - The root of the chord is G, so we'll refer to the G major scale and then modify as necessary to make the chord minor.
(The G major scale is G A B C D E F#)

Step 2 - Apply the 'minor chord formula' to the G major scale
The formula for minor chords is 1 b3 5 which produces the notes G Bb D.

Step 3 Place the notes G Bb & D anywhere on the fretboard within reach of your fingers.

Remember, you only need those three notes (G Bb & D) in any order to produce a correct G minor chord. But on guitar, we normally want more than three notes for a fuller sound, especially if we want to strum it. So, we can double any of those notes, higher or lower.

Examples
XX5333 = X X G Bb D G
355333 = G D G Bb D G
355336 = G D G Bb D Bb
XX0333 = X X D Bb D G

Root position and inversions
Notice that in all of those examples apart from the last one, the lowest note is also the root note. This is the most common way to arrange chords, because when the root is the lowest note, the chord sounds more balanced. In that arrangement, the chord is said to be in 'root position'. If any note other than the root is the lowest note, then the chord is said to be inverted as in the last example. Inverted chords (or inversions) sound less balanced or solid, so are used much less often. Sometimes, though, you might actually want a little less solidity in the chord, perhaps for a more delicate sound, or you might want a certain bass note other than the root as part of a bass run, in which case you'd use an inversion, such as the last G minor example.
Sometimes in chord song sheets, you're required to play the chord inverted - this is often shown with a slash followed by the required bass note, such as Gm/D. It's still a G minor chord but the bass note has to be D.