How to search for a person on facebook with no mutual friends?

[Nancy]

You can't find him because you don't have his information. You will not find him with just a first name. I don't get why you have a birth date, but didn't think to ask his last name.

You were both on holiday. Most people don't want to get involved with someone they meet on holiday, so they either give a minimum of information or they give false information.

Did you give this person your full name? If so, if he is interested in finding you, he will look you up. If not, you need to just chalk this one up to a one day/holiday fling. The only way you will find him is if you happen to holiday in the same place at the same time again.