Washington
There are a large number of private research groups (often known as the Beltway Bandits, from their location on the Beltway highway around Washington and their dependence on government contracts) and pressure groups of every political stripe in Washington with interests in foreign affairs. Hiring is informal, so internships are important for anyone interested.
International Business
Multinational corporations play a prominent role in current international affairs. Most Americans tend to think in terms of working abroad for an American corporation, but in fact there may well be better opportunities working in the U. S., either for an American or perhaps even a foreign firm (of course, that may not be what you think of as an international job).
American corporations used to send significant numbers of Americans abroad, where they were often something of a trial. They were expensive, had a high failure rate (sometimes as high as 50%), did not want to stay long, did not know the language, and often alienated foreigners. Moreover, the corporations did not know how to use the people with international experience when they got back and often essentially punished them for going abroad. Thus most corporations moved to develop indigenous managers (Norwegians to run Exxon Norway, Nigerians for the Coca Cola branch in Nigeria, etc.) and to reduce the role of Americans abroad.
Recently there has been something of a reaction against this trend, although different corporations have different policies. The number of Americans being sent abroad is certainly smaller than it used to be; better selection and training has reduced the failure rate. People with particular technical skills are often sent abroad. In addition, many companies are re-developing international assignments for their fast-track managers because of the importance of foreign markets. It is unlikely that an employee will be sent abroad by a large American company unless they fall into one of these two categories.
The other side of the coin, of course, is that foreign companies doing business in the U. S. hire many Americans. Moreover, an increasing percentage of American corporations do business abroad, so much "normal business" in the U. S. involves international issues. In general, if students want to go into business, they need a Masters of Business Administration (MBA) degree from the best business school they can get into; this degree and some alternatives are discussed later. If interested in working for a foreign company, knowledge of its language and culture can be invaluable, but it is no substitute for business training. Nobody is going to hire an individual just because they know the appropriate language; they have to also think the candidate will raise their profits.
Among businesses, international banks have been the most willing to hire people without business degrees; they expect to have to train employees regardless of their background. Another alternative is analyzing the political risks of investments in particular countries. There are some jobs here within corporations and at consulting firms; however, relatively few people have been hired, and it is not clear that they will be able to move up to other jobs within the organization.
Non-Profit
There are literally hundreds of private, volunteer organizations which work in international affairs; they are so important that they have been awarded the ultimate distinction of their own acronym, PVOs. Some of the PVOs are religious in origin; others are entirely secular. Some are quite large, others are minuscule. They share a lack of direct government control and general concern for humanitarian issues. Prominent examples include Crossroads Africa, Oxfam, Catholic Relief Services, and Maryknoll. The American government administers some foreign aid through some of these agencies, and they have been prominent in such issues as famine relief in Africa. The PVOs overlap somewhat with private advocacy organizations such as Amnesty International. Many of these organizations employ small permanent staffs; recruitment is often based on previous performance as a volunteer. Salaries are low, but many people find the work extremely rewarding.