If you want to do voluntary service in Hungary the best to start with is the European Voluntary Service (EVS). EVS is the part of the Youth in Action Programme which is the EU Programme for young people aged 15-28 (in some cases 13-30). You can also find some other opportunities among the links below.
What is EVS about?
Open to all young people aged 18 to 30, EVS is a true ‘learning service’. Beyond benefiting the local communities, by participating in voluntary activities, young volunteers can develop new skills and, therefore, improve their personal, educational and professional development. Volunteers can benefit from specific training throughout the activity and agree on their expected learning outcomes, processes and methods in advance. Their learning experience is formally recognised through a Youthpass. Participation is free for the volunteers who also get board and lodging, insurance cover and an allowance for the duration of the project. Special conditions apply to encourage the participation of young people with fewer opportunities. For instance, they can participate as of the age of 16. See some reports of previous EVS volunteers at the Report section.
How to participate?
A successful EVS project requires close co-operation among at least three key players: a sending organisation, a host organisation and the volunteer. One of the organisations involved in this partnership also plays the role of coordinating organisation and applies for an EU grant on behalf of the partnership. Organisations perform a number of roles: they identify volunteering opportunities and develop projects that benefit the local community. They also recruit and prepare the volunteers, host them, and ensure follow-up.
EVS activities can be carried out both individually or in group. Up to 100 volunteers can now participate in the same EVS activity!
The European Voluntary Service spans a wide range of areas, such as culture, youth, sports, social care, cultural heritage, the arts, civil protection, the environment, development co-operation, etc. One thing all the activities have in common is a clear European and intercultural learning dimension. EVS is a mutually beneficial process, where everybody gains from getting to know the other's culture.

http://ec.europa.eu/youth/youth-in-action-programme/doc82_en.htm
The European Voluntary Service (EVS) provides young Europeans with the unique chance to express their personal commitment through unpaid and full-time voluntary activities in a foreign country within or outside the EU.
http://ec.europa.eu/youth/evs/aod/hei_en.cfm
Search for hosting organizations and projects with the help of this database.
http://www.evsguide.eu/int/youth-in-action/evsguide/index2.html
This booklet is a guide for young people who are thinking about participating in European Voluntary Service, and their organisation(s).
http://www.salto-youth.net/eecaA2/
A short summary of European Voluntary Service on SALTO website.