I drink green tea everyday at work. I fill my 2 liter tea pitcher with hot water from the sink, and put two bags of tea in it (I like Celestial green tea with white tea, because the white tea gives it a little extra flavor). I usually give it about 5 minutes to steep and then I start drinking it (I never remove the tea bags, though; it's not necessary). I don't use sugar or anything else in it.
Things to know about making green tea:
1. Don't use boiling water; green tea is best used with hot, but not boiling water.
2. Don't use too much/oversteep. Green tea is bitter if it's too strong. That's why I only use two bags for an entire pitcher and I let them steep completely. If you use a lot of bags for one pitcher, you must be very careful to only let it steep for about a minute, then remove them (I find this is not only tedious, but it's wasteful; why use a small portion of the tea leaf's power, then throw the rest away?)
3. Really good green tea has an electric yellow/green tint. Most of the stuff you get in the grocery store comes out a light brown. While that's drinkable, nothing beats a proper green tea. Look for some at an international grocery store or online.