Do NOT swing your head on your neck if you are seriously going to headbutt someone. It might work like that if you are just smacking their nose from up close, but if you are going head-to-head, you are setting yourself up for serious neck damage. Swing from your waist or push up with your legs. Targets should include the nose, temple, or side of the jaw.
Some strike with the forehead, I’d prefer the top of the forehead, just at or above the hairline. Striking with the top of the head (Ram-Man style) could damage your spine, not recommended.
Practice on a heavy bag to find out what works, and if you seriously injure anyone, even on accident, be prepared to face assault charges.