Learn French: Son bureau est au septième étage. - His office is on the seventh floor.

In English, you say someone is "on" a floor, but French uses the preposition à to indicate which floor a room is located on. Because étage is masculine, à and le contract into au.

Does son bureau mean the office definitely belongs to a man?

Not necessarily. The possessive adjective son agrees with the masculine noun bureau, not with the gender of the owner. Without more context, this could just as easily translate to "her office".

If I am in an American building, would this correspond to the seventh floor?

It would actually be the eighth floor! In France and most of Europe, the ground level is the rez-de-chaussée. The premier étage (first floor) is one flight of stairs up.

Is there a simple rule for making ordinal numbers like septième?

Yes, you usually just add the suffix -ième to the number. If the number ends in an "e" like quatre, you drop that "e" first to make quatrième.