This is my go to recipe for excessive basil. It is relatively quick and easy not to mention extremely refreshing. You can vary its sweetness to your own taste by adding more or less sugar to the water. I use Spenda to make it "healthier" as I do drink a lot of it.
Bring 6 cups of water to a boil in a medium pot. Add the tea bags and let it steep for 20 to 30 minutes. Time can vary but you will be able to tell by the darkness of the water when it is done.
At the same time you are preparing the tea, add the cup of water and Spenda to a boil, stirring till the sugar dissolves. Turn off the heat and add the basil.
Once everything is completed, remove the tea bags from the one pot and the basil from the other and combine in a pitcher. If it is plastic make sure you let it cool enough not to cause any trauma to your pitcher. You can leave the basil in the water until it cools enough to combine. The longer the basil is in there, the more it will infuse so you really can't go wrong. Put it in the refrigerator and chill till you are ready to serve.