What would be the most common massage techniques for getting rid of headaches and migraines?

AcuPressure/Puncture: There are many points that reduce headaches. Place pressure on the fleshy part of the hand between the thumb and index finger, pressure on the back part of the skull, in between the eyebrows while moving upwards along the center of the forehead, apex of the scalp. Would recommend speaking with someone certified in acupuncture/acupressure for best results.

GUA SHA: You have already been provided with good ideas. Gua shat is super for tight/ tense neck, head, shoulder muscles. Gua _sha > scraping with a buffalo horn is the best pain you have ever felt. It is practiced by many acupuncturists. My patient's swear by it. However, don't be surprised if you get bruised. It is well worth it. This is a recommendation for tension headaches (not migraines).