The actual mechanics vary between the different makes of capo. For
instance, I use a Shubb capo which consists of a curved metal bar
with one "hinged" arm and one pivot arm in a curved "E" shape. The
capo is placed just behind the fret. The main bar is fitted with a
rubber sleeve which covers the strings, and the hinged arm fits behind
the neck. The pivot arm has an adjustable screw which pivots on the
hinged arm locking the capo in place. The adjustable tension screw
can therefore be adjusted to fix the capo at different positions on
the neck without using excessive force which could cause damage.
If we place the capo behind the first fret, all the strings have
been raised by a semitone. If we play a G chord shape, you are really
playing a G#/AB chord. If we place the capo behind the second fret,
all the strings have been raised by a tone. If we play a G chord shape,
we are really playing an A chord. If we place the capo behind the
third fret, all the strings have been raised by three semitones.If
we play a G chord shape, we are really playing a A#/Bb chord and so
on.
Can you spot the pattern? If we place the capo at fret "x", whatever
chord we play will be "x" semitones higher. This principle also applies
in reverse, so that if we place the capo at fret "x", we play a chord
"x" semitones lower than the one written.
For instance, suppose a song has Eb, AB and Bb chords in it. We could;
Place the capo at the first fret and play E, A and B chords respectively,
Place the capo at the third fret and play C, F and G chords respectively,
Place the capo at the sixth fret and play A, D and E chords respectively
etc etc.
It is important to remember that any chords and tablature are played
relative to the position of the capo - for instance, if the capo is
placed behind the fifth fret, a G chord will written as 320003, even
though the actual frets are 875558. If you visualise the capo as the
nut, this approach makes sense, and allows you to think in terms of
more familiar keys, chord shapes and patterns.