Many schools abroad require teachers to have TEFL (Teaching English as a Foreign Language) certification or an advanced degree in second language acquisition. Many schools in the United States as well as distance learning programs lead to both. TEFL certification and graduate school are significant commitments, but the advantage is that you will be more marketable with an advanced degree or certification. The disadvantage is that if you plan to spend one summer abroad the time spent earning the TEFL certification or a graduate degree may not be conducive to a short-term goal.
Entering "teach English abroad" in any search engine will lead to hundreds of links with teaching jobs that require little to no experience. Being a native English speaker with a bachelor's degree is sometimes the only prerequisite. Those without a bachelor's degree are also eligible to teach English in some locations.
Many religious organizations abroad need English teachers for summer projects. This works well for students who are unable to spend a year or two abroad, but would like the exposure of teaching in a foreign country. These trips can be between four to eight weeks and vary in location.
You may be able to embark on your journey with all expense paid if a private language school is offering you employment. These schools normally have wealthier clientele, hence your flight and living expenses are paid for and you will earning a stipend. Be sure to that the organization you choose is reputable.
If you're looking for a short-term Peace Corps-like experience, consider working as a volunteer for a non-profit organization. Countless organizations need volunteers to teach English to youth. An additional perk is that teaching can be combined with such other fun activities as building bridges or a school library.
If none of these options seem viable, consult the websites of international education organizations or institutions of higher learning where you will find teaching opportunities that suit your interests and needs.