Complex sentence: In New York Cooke quickly became a master of the techniques given in Dianetics, and subsequently met Mary Oser, who had flown to New York from Switzerland seeking a competent practitioner of Dianetics to treat her husband.
Split into simpler sentences: In New York, Cooke quickly became a master of the techniques given in Dianetics. He subsequently met Mary Oser, who had flown to New York from Switzerland seeking a competent practitioner of Dianetics to treat her husband.