If you plan to hire a car in Amsterdam or Cyprus, be prepared for an experience unlike any other you have ever had. Amsterdam can be a very difficult and confusing place to drive if you are unfamiliar with the city, but it is not impossible if you are adventurous and have a very good map. Cyprus can also be challenging in the narrow streets of the smaller villages, but in the major cities a good map and a bit of patience will get you most places you need to go.
In either place, hiring a car requires you to show your national driver's license and current proof of insurance coverage. A few other things to consider:
Which side of the road should you drive on? (Amsterdam/right, Cyprus/left)
What do the various road signs and warning signs mean?
Are there regulations about wearing seat belts, using car seats for children, etc.?
Check out your local library for more information in advance of your holiday travel, and be sure to ask the car hire company for a driver's guide once you get there.