Once you arrive in your host country and exit the plane, you will be required to go through immigration. This typically requires that you show your passport and any required visas and/or immunizations to an immigration official. It is important to be respectful and cooperative as your proceed through this process, especially when security is heightened. The immigration official will check your authorization and stamp your passport. They will typically ask the purpose and length of your visit.
Once you proceed through immigration, you will collect your luggage and go through customs. Your luggage may be x-rayed or physically searched. It is also possible that you will be simply waived through customs without having your luggage searched. DO NOT MAKE ANY JOKES ABOUT BOMBS OR SMUGGLED ITEMS. This is taken very seriously and even joking about this will cause you serious delays and perhaps even jail time.
If you are stopping in a country between the United States and your host country, you may be required to go through this process in that country as well.