Construct an idea of what global citizenship means to you and in the context of your classroom or school. If it is something that your school has discussed, you might have a definition of it, such as "A global citizen is a person who is aware of and who cares for the entire Earth." If you don't have a definition, come up with one so that you might teach that definition to students.
Teach students about diversity from the first moment you have them in the classroom. Students should learn about different cultures, different races, and different religions. They should also learn other types of diversity, such as political diversity. The more diversity a student is exposed to and understands, the more global the student will become.
Teach students about the world in general, the geography, the countries, and the people who live there. Help the students to see life as something that exists on a global scale, and not just on a local scale.
Explain to students some of the issues that face the world at large, not just issues that face those particular students. Talk about hunger, the fight for clean water and global warming. Discuss alternative fuels, the space program, and international trade, along with other matters that affect more than just the people in one particular place. Help the students to see that the world is comprised of many different people working together to solve many different problems.
Explain how global issues can trickle down to local issues, and give students concrete tasks that they can do to become global citizens, such as picking up the playground to free it of trash -- one small step in the fight against garbage in the world. Students should learn that to be global citizens, they can begin by focusing close to home, and move their way into positions to focus on larger issues.