Green tea is usually steeped between two to three minutes and not a minute more or you risk bitterness. Depending on the type of green tea, you steep for no more than 30-60 seconds, mainly matcha (because it's a powder and not a leaf).
Hmm, did not know that. Is green tea supposed to taste pretty subtle then, cause I swear when I make it I can barely taste it unless I have it steeping for quite a while. Or perhaps I'm just buying bad quality tea.
Tea bags or leaves? If you're using bags, try to go with pyramid shape tea bags.
The key to green tea is circulation. Let it flow in the water.

The benefit of pyramid is that it lets the leaves go all over and spread around the bag. This is true for all tea and not just green tea, but green tea is really tricky. Also, another pro-tip. If you using a tea bag remember to dip after steeping to get the taste out. If you're using a tea bag make sure it's like the bag above: clear and transparent. The other teabags tend to filled with dust and you can't see what's in them.
If you're usng leaves, use more leaves. More leaves is better than steeping longer.
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I'm not a snob or anything but the quest for making the perfect cup of tea is a personal and fulfilling one. It's fun.
You tea could dependent on a lot of factors: water quality (make sure it's filtered tap or fresh water), water temp (green tea is best when brewed at a cooler temp than black tea). If you're using tea pot/kettle, remember to wash them out ;etc