I suppose the karyotype and hormonal (FSH, LH, testosterone) examination in the first line. The cause of azoospermia may often be the Klinefelter syndrome (47XXY) as well as structural chromosomal anomalies or the hypophysal hypogonadism. Then the DAZ gene (AZF), other causes are more rare, gr/gr deletion on the chromosome Y, DAZL on the chromosome 3 (3p24), E2F1 on the chromosome 20 (20q11.22) etc.
there is a good paper of Martin M Matzuk & Dolores J Lamb (The biology of infertility: research advances and clinical challenges 2008) in which they collected those genes in a box2