There are three very good rules when it comes to dealing with the customs officials of another country:
In fact, these rules also apply to dealing with the customs officials of your own country too. In the case of the United States, it is often difficult to find the information you need because the rules are always changing and links to their needed spots on their websites seldom stay put for more than a year. The best you can do is to do your best, answer their questions honestly, and don't get upset.
What follows comes from the references shown below. Where I think it helpful, I've added my own comments in blue.
You will probably need a passport to enter another country and then to return to United States. The rules are different for each country and can also change depending on the other countries on your itinerary. The rules of Visas can also be different for passengers and crewmembers. You may be surprised to hear that many countries even have rules on how many blank pages must be available in your passport or how many months remain before expiration. The best way to be certain is to visit: http://travel.state.gov/content/travel/english.html and use the "Learn about your destination" section.
A person who enters the United States under the Visa Waiver Program may not be aware that they cannot depart the country unless the entity providing the transportation is approved under the program. Even as a 14 CFR 91 operator you can be an approved Visa Waiver Program carrier, but even if you aren't and one of your passengers is travelling using the Visa Waiver Program, you need to be smart about it. More about this: International Operations / Visa Waiver Program.
Some countries required minors traveling without their parents have notarized travel permission from their legal guardians.
Getting into and out of Canada is fairly easy and it can be even easier if you, everyone on your crew, and all your passengers are enrolled in CANPASS. See: CANPASS.
You've got no choice in the matter anymore, you have to participate in the Electronic Advanced Passenger Information System (eAPIS). An international flight planning service can make this easy for you, but you can do it yourself. The system the Department of Homeland Security (DHS) gives you through Customs & Border Protection (CBP) is fair, at best, but it does work. It won't remember your passengers or crew, but it remembers you. Several flight planning services that you are probably already using can automate things and make the entire process a bit less painful. More about this: International Operations / eAPIS.
The process of getting back into the country has gotten easier, thanks to the proliferation of electrons in the system. Things will go more smoothly if you have eAPIS complete, have your paperwork in order, and be patient with the guy wearing the badge and gun.
You can't depart for the United States unless you have your eAPIS in order. More about this: International Operations / eAPIS.
[14 CFR 61] §61.3 (l) Inspection of certificate. Each person who holds an airman certificate, medical certificate, authorization, or license required by this part must present it and their photo identification as described in paragraph (a)(2) of this section for inspection upon a request from:
The customs and border inspector will ask for your pilot's license, medical, and a photo ID which is normally your passport.
Foreign visitors to the U.S. arriving via air or sea no longer need to complete paper Customs and Border Protection Form I-94 Arrival/Departure Record or Form I-94W Nonimmigrant Visa Waiver Arrival/Departure Record. Those who need to prove their legal-visitor status—to employers, schools/universities or government agencies—can access their CBP arrival/departure record information online. More about this: http://www.cbp.gov/travel/international-visitors/i-94-instructions.
Declare all articles on this form. For gifts, please indicate the retail value. Use the reverse side of this form if additional space is needed to list the items you will declare.
The U.S. Customs officer will determine duty. Duty will be assessed at the current rate on the first $1,000 above the exemption.
Read the notice on the reverse side of the form.
Sign the form and print the date.
Keep the complete form with you and hand it to the CBP inspector when you approach the Customs and Border Protection area.
This form is required at only a few points of entry, KPBI to name one. To date, there is no central location of information detailing when the form is needed. Just make sure you’ve got one per crewmember at KBPI!
Forms available at: http://forms.cbp.gov/pdf/CBP_Form_5129.pdf.
They say the Gen Dec is no longer required in the United States, it has been replaced by eAPIS. More about that: International Operations / eAPIS.
The trouble is much of the rest of the world still requires them and the form is still in print, available here:http://forms.cbp.gov/pdf/CBP_Form_7507.pdf.
Portions of this page can be found in the book International Flight Operations, Part VIII, Chapter 16.
14 CFR 61, Title 14: Aeronautics and Space, Certification: Pilots, Flight Instructors, and Ground Instructors, Federal Aviation Administration, Department of Transportation