I start every single morning with a cup of piping hot, fresh homemade chai. I feel the same way about chai that most people feel about coffee - can't start the day without it. While it does take a little while to make a proper cup of chai, it's actually very easy and worth the time. One word of warning, though: once you start making your own chai, you become a chai snob and can't drink that sickeningly sweet "chai" served at most coffeeshops.
There are as many ways to make chai as there are people who drink it, and I've played around quite a bit with different recipes. Below is how I've been making it for a while now, but there is no right or wrong way to make it. I don't measure anything, so the amounts listed are very much an estimate.
2 cups of water
3" piece of fresh ginger, peeled and sliced
about 5 whole peppercorns
about 10 whole cardamom pods
1 tbsp black tea
1/2 cup milk
jaggery to taste
Put water and ginger in a saucepan and bring to boil. While waiting for it to boil, crush peppercorns and cardamom in a mortar and pestle; add to water once it boils. Turn down the heat and simmer for ten minutes, then add the black tea and simmer for five more minutes. Add the milk and bring to a boil three times (bring to boil so that it almost overflows and then carefully move it away from the heat and let it settle back down; do this two more times). Sweeten with jaggery and stir well, then strain and serve.
Oh, and please please please don't call it "chai tea." Chai means tea, so saying chai tea is super redundant!