Man greeting Man - Men greet one another with a warm handshake (right hand only) using, embrace and possibly one to three kisses on alternating cheeks depending on the level of familiarity.  For foreigners it is best to start with the handshake and follow the lead of your Saudi counterpart if kisses are offered.  Handshakes often linger a bit and may continue while walking.  In certain regions of the country, kissing the shoulder of a superior/elder is customary.  This also customary when meeting members of the Royal family.  If greeting an older family member (father, grandfather, etc.) one might kiss their forehead to show respect.

Woman greeting Woman – A handshake (right hand only) is common and possibly one to three kisses on alternating cheeks (once on the right, then twice on the left) depending on the level of familiarity. Some women do both cheek kissing and hand shaking, depending on the group of people, and how familiar they are with each other. If greeting an older family member (mother, grandmother, etc.) one might kiss their forehead to show respect. 

Greetings between Men & Women - There is little to no touching between men and women during greetings in public, unless related by birth or marriage, and even then it tends to be minimal.