A word of advice: many of these parties are not advertised.
You may need to speak to an embassy employee or fellow countryman in the kingdom and ask them to add you to the list, since these parties are by invitation only.
Dating in Saudi Arabia is really no different in this respect, but there are a few things you should keep in mind. You should make continuous eye contact, but be wary of mall security at the same time.
First of all, you are not legally allowed to just walk up and talk to a girl. Follow the group or, if they are following you, make sure you occasionally make eye contact to signal interest, and then go somewhere discrete, like a unisex store. Saudi girls may initially be shy, but many won’t hesitate making the first move (kind of a paradox there) and hand you their phone number.
You will often see the picture of some flower or artsy pic instead on her profile.