Citizens of the United States need passports to travel to other countries including Canada and Mexico. Applications can be found here.
Be sure to allow sufficient time for processing. If you are even considering studying abroad, make your application early – 4 to 5 months in advance. Current costs are $97 for a new passport and $67 for a renewal.
Depending on the time you intend to stay overseas, you may need a visa for the country before you depart for your study abroad experience. This will take additional time for processing. Information by country about whether you will need a visa can be found here.
Note that even though two countries are in the European Union, their visa rules can (and probably will) differ.
Be sure to know what the US Department of State travel warnings (if any) are for each country you plan to visit. These travel warnings are updated regularly and can be found here.
Another useful link containing tips for traveling abroad can be viewed here.
Be aware of your surroundings for safety. Do not knowingly put yourself into dangerous situations. Be careful and aware of your personal belongings (wallet, money, credit cards, luggage) while you are traveling. Do not accept anything from anyone to carry for them. Airports and tourist areas are popular sites for thieves and pickpockets. If you do consume alcohol, do so in moderation. Alcohol can affect your judgment adversely. Avoid demonstrations and political rallies. They can turn violent.
Depending on the countries you will be visiting, you may need to have immunizations if you will be staying for an extended period of time. The Center for Disease Control has information about recommended health measures before you travel and while you are traveling overseas. Your state Board of Health may also have recommendations. Check with your doctor for specifics. In any case, you will probably want to be certain that you have an immunization against tetanus within the past five years.