First of all, "chai" means tea in India. It is usually made with a blend of spices, tea and milk. "Oregan Chai" did not invent it, and is less like the original than most bagged chai teas.
I've tried a couple of ways to make my own chai tea. Spices can either be mixed and added separately or you can find a bagged tea of your preferred spice level.
Ready-made spice mixes:
These can sometimes be found in the bulk section of a grocery store or boxed at an Indian grocery. If you see something called Masala Spice or Garam Masala, don't be fooled into think it is for tea, because it has spices that are better for curries. Masala Chai or a box with tea on it is the label you should look for:
MDH T-Plus Masala
Badshah Kamal Tea Masala
Spice mixes are meant to be brewed wit the tea, not mixed into your tea cup. It's very easy to go overboard adding it to a cup. Spice can be added to a mesh tea ball or strainer with black tea leaves and steeped with the tea. The first time I bought spices, I didn't know this and put a whole teaspoon in my cup which was like drinking hot black pepper.
For something closer to what you'd find in Indian restaurant, put your tea leaves and spice in a tea ball or fillable tea bag and brew in a pot on the stove directly in a mix of water and milk (bagged tea will work just fine too, but you may need more than one). I usually use 1 cup of milk to 1 1/2 cups of water. Honey or sugar can be added as you like.
Making your own spice mix:
Using a list of the spices traditionally used, find them in a grocery store and make your own mix. Some of the spices will probably come whole and need to be ground. My favorite recipe came from a Steampunk blog and involved grinding and roasting the spices in a pan before using: Kagashi's Kitchen: Masala Chai Mix
Pre-mixed loose and bagged teas:
If you prefer a pre spiced tea, there are many available. There is a lot of variation in brands of chai tea and the recipes used at coffee shops. For a long time I wanted to make a list of the spiciest to the blandest in my opinion, so here goes.
• Your Local Indian restaurant's chai will probably come mixed with milk, but without any sweetener.
• Frontier Organics Chai A loose tea with fine ground spices mixed in. Needs to be strained well before drinking. Can be found at some Rainbow and Copps stores in Minnesota and Wisconsin.
• Stash Double Spice Chai Spicier than their regular Chai bags.
• Yogi Tea Chai Yogi and Stash seemed pretty similar to me.
• Stash Chai Stash carries both, bagged and loose online. The bags can sometimes be found in locally.
• Celestial Seasonings India Spice Chai Can become very spicy if left to steep a long time or with more than one bag.
• Bigelow Chai
• Tea Source's Reena's Chai A loose tea.
• Tazo Chai Tea bags
• Adagio Masala Chai Tea
• Teavana Chai
• Starbucks Coffee - As far as I know uses Oregan Chai concentrate, which is good if you like sugary pumpkin pie flavor, without a lot of spice. This was probably the first chai I encountered, so I can't say it's horrible.
• Oregan Chai mix - This is a liquid concentrate that Starbucks and a lot of coffee shops use. It's already sweetened (a lot), so if you prefer less sugar it's probably better to brew your own another way.
• Caribou Coffee - The last time I had a Caribou Chai, I saw the sign that said "New Milder Flavor!" too late. That was the last time I drank any. They decided Minnesotans couldn't handle spice and replaced it with hot nutmeg water.