Start by gripping a set of rings (these are the safest way to do chinups - they allow your arms to rotate through a natural motion), alternately you can use a bar. These should be overhead and your hands should be about shoulder width apart.
Breath out and squeeze your shoulder blades together and down your back. This sets the shoulders in place. When your entire bodyweight is hanging from them, it is best to have muscles supporting the shoulder joint rather than just the ligaments.
As you reach the top of the movement, twist your forearms so that your palms face toward yourself (rings only).
Breathe out as you return to the start position. Do the movement at a comfortable breathing pace.