One option for volunteering in another country is to go with a volunteer-sending organization or program. These organizations coordinate international volunteer roles and projects and will often also arrange such logistics as housing, in-country transportation, and meals.
That said, there is a lot of variation—both in terms of what is provided as well as in price—so you'll want to spend some time researching and comparing to decide what structure or type of program you might want to volunteer with.
Examples of nonprofit volunteer-sending organizations include VSO, WorldTeach, Cross-Cultural Solutions, United Planet, and Global Volunteers.
Examples of for-profit volunteer-sending organizations include Projects Abroad, i-to-i, ProWorld Service Corps, Global Crossroad, and Volunteer Adventures.
Examples of faith-based volunteer-sending organizations include Catholic Network of Volunteer Service, American Jewish World Service, Mennonite Central Committee, and the United Methodist General Board of Global Ministries. (If you're seeking information on volunteering with a Christian organization, consider checking out the directory and training resources at ChristianVolunteering.org)
Examples of voluntourism organizations include Globe Aware, Bike & Build, and Voluntouring. Programs and packages are also increasingly offered via hotels and traditional travel companies and websites.
Examples of study abroad organizations with a service option include the International Partnership for Service-Learning and Leadership (IPSL) and World Learning.
Examples of organizations offering both volunteering and language components include AmeriSpan and BridgeLinguatec.
Examples of companies with international employee engagement programs include Timberland and IBM.
So as you can see, there really are many different volunteer-sending organization types and structures. Take your time and consider your options, then 1) start identifying potential organizations and programs, 2) do your research, and 3) ask questions to determine if they are a good fit for you.
Does it matter whether the volunteer-sending organization is for-profit or nonprofit?
Some volunteers choose a nonprofit volunteer-sending organization because it was formed primarily for the public good. Others have no preference for nonprofit or for-profit, instead focusing on finding the volunteer program, regardless of structure, that offers the location and service opportunity they are looking for.
At the end of the day, it comes down to doing your research. Prices vary widely whether nonprofit or for-profit and there are ethical, mission-driven organizations on both sides, just as there are for-profit and nonprofit volunteer-sending organizations that could do a better job of arranging quality, sustainable service opportunities. Ask the questions that are important to you and you should be able to find the volunteer-sending organization whose mission, practices, and opportunities are the best fit for you.