international drivers license

Yes.
It's not a license, it's called International Drivers Permit and is just a translation of your license in multiple languages (you need to carry your home license with you).
The car rental office may not ask you for one, but if you get stopped by the police or get into an accident you'd better have one or they will fine you or maybe arrest you.
It takes 10 minutes to get one at any AAA office, all you need is $15 and 2 passport photos (which AAA can take for you for additional $10). It's valid for one year, so get it just before your trip.

And to add to what Roberto has said, each driver needs the permit.

It's exactly as Roberto says. If you are a member of AAA you get discount. So instead of $25 if you don't bring pictures I paid $20. I just had one done because I was in the neighborhood of AAA even I will need it in June. Then I asked to start validity June 1st.

So, it would cost $25 per country? does that include the $10 for the photos? Even if it does include the photos, it would be $75 (for 3 countries) for each driver ($150 for both)? How long does it take for them to process the order?
that seems rather expensive. Are there any other ideas as to where we might get this service for less money?

It is International Driver's Permit therefore you don't need Permit for each country. It is for all just one Permit. It cost $25 if you don't bring pictures and don't have AAA membership. It's not expensive. $25 per driver. If you bring your photos and are member of AAA then it's significantly cheaper. You come to AAA, they take picture, you fill the application: name, address, date and place of birth, drivers license number. All takes about 10 to 15 minutes and you are leaving AAA office with your fresh International Driver's Permit.

It gets expensive when you don't have it. A few months back someone posted on this site that they were involved in a minor traffic problem in Italy. Didn't have the permit. The fine was 500 Euro and the local police threaten to impound the rental vehicle. Understand he talked his way out of that. In the US we tend to take traffic infractions lightly. "Give me the ticket. I will mail it in." Europeans have a much sterner view of law breakers especially the petty ones. And collecting fines on the spot is standard and not a scam. Get you head around the idea that you are not in Kansas anymore.

And, I believe, that AAA is the only one authorized in the US to produce permits. The ones offered in the internet are fraud.

royal,

The others have provided good information on the International Driver's Permit. As mentioned by Ilja, you don't need a separate permit for each country, one covers them all and the permit is valid for a year.

One other point to mention is that the I.D.P. is used in conjunction with your home D.L., so you must bring that as well.

Thanks to everyone. I had read some previous forums on the same subject. I am wondering what the purpose of the permit is. Is it printed in English? Some people indicated that is was so the police could read it, that is why I thought I would need a separate one for each country. Linda

What the IDP does is translate your drivers license into a variety of languages. That way if someone needs to know if your license is valid they don't need to speak or read English to determine that. You carry it with your US drivers license, not instead if it.