I have done this several times with Chinese university students. I find it helpful to write some category headings on the board before the class. I divide organisations into:
general e.g the UN
economic and trade e.g WTO, IMF, World Bank
charity and culture e.g UNESCO, Oxfam, Red Cross
Commoditiies e.g OPEC
Regional e.g ASEAN, EU, NAFTA
Military e.g NATO
Then I elicit which organisations the students already know. In China this takes patience because the Chinese have a habit of trying to transcribe the names into equivalent Chinese sounds but inaccurately. On othe roccassions the students will know the initials but not what they stand for. Then I fill in the gaps. I always also have a map of the world on the wall when doing this.
Stage 2 is to select a few of the more important organisations relevant to whatever the students are studying. I was mostly teaching business so focused on the economic and trade organisations.
Then I either use powerpoint presentations or if their is no equipment make a table on a large white board and fill in details such as membership, leaders, location, aims, strengths and weaknesses etc. How much you lecture and how much you try to elicit from the students will depend on their English level especially listening skills. Be careful to write unfamiliar words especially names on the board. Most students in China can �t transcribe them from sounds and won �t tell you this.
It is important to encourage the students to take notes and to pace the lesson to allow them to do so.
You could also give out a handout of websites about the main organisations and an internet based research and writing task for homework.