The U.S. Embassy in Costa Rica hires locally for a very small number of administrative positions, and openings are fairly infrequent. Employees hired locally are paid local salary rates and are covered by Costa Rican labor laws. See the Embassy of Costa Rica's work permits page for info in getting a work permit to get a job on the local market. The Department's internship program offers the possibility to work in many different countries, including Costa Rica. There are some Americans here who teach English in the many private language schools.
Wages are low by U.S. standards.
If you have elementary or seconday education certification, there are several private English-medium schools here that hire locally and from abroad. If you are interested in teaching school in Costa Rica or another foreign country, see the Department of State's Overseas Schools page for a list of recruiting organizations and for information on schools that are supported by the U.S. Government overseas. The Peace Corps has a small number of volunteers in Costa Rica. Other U.S. non-profit programs such as WorldTeach have placed volunteers in Costa Rica in past years. The Embassy has no specific information on volunteer opportunities at this time.