I love love love basil tea. I learned about it when I was looking for ideas to use the flowerheads I pick off the plants. (I don't let them bloom because it makes the leaves bitter.)
Here's the method I use to brew:
1. Harvest blooms or leaves.
2. Muddle with a couple tablespoons of sugar. This releases all the great flavor.
3. Pour cold water over the leaves.
4. Add sweetener to taste. I use different ones depending on my mood. I like raw sugar, honey, agave or stevia.
5. Leave it in the fridge for several hours. At least 8, but 24 is better.
You could use hot water like regular tea. But I think that changes the flavor.
You could also use basil to flavor regular tea-leaf tea.
It's the perfect drink for sipping while sitting on the balcony, watching the sky darken, and feeling the first cool breeze of the evening.