Using the E(m) and A(m) shapes, the chords in a key come in two L-shapes. Two of the major chords will be an E and an A-shape on the same fret (one of which is the I-chord), and then the third major chord is the E-shape 2 frets lower or the A-shape two frets higher (depending on which was the I-chord). The three minor chords form a similar L-shape.
In a major key, the major chords are located like this:
| | A | | A | |
| | E | | | |
if the E-shape is the I-chord, or:
| | | | A | |
| | E | | E | |
if the A-shape is the I-chord. The minor chords are located in a similar L-shape like this:
| | | | Am| |
| | Em| | Em| |
or:
| | Am| | Am| |
| | Em| | | |
which gives us these combinations:
| | A | | A | | Am| |
| | E | | Em| | Em| |
or, lower on the neck:
| | Am| | Am| A | | A | |
| | Em| | | E | | | |
if the E-shape is the I-chord, or:
| | | | A | | Am| | Am| |
| | E | | E | | Em| | | |
or, lower on the neck:
| | | | Am| | | A | |
| | Em| | Em| E | | E | |
if the A-shape is the I-chord.
The same four combinations of major and minor L-shapes also work for minor keys. Combination 1 and 4 when the Am-shape is the i-chord, and combinations 2 and 3 if the Em-shape is the i-chord.
These L-shaped pattern are easy to memorize, so once you've located the chord that is the I or i-chord in the key, the other chords are easily located. Using just the A(m) and E(m) shapes may be a little simplistic, depending on your level, but I think it's the easiest way for a beginner to quickly figure out the chords in a key and be able to play along with others or a recording.