Buy a plastic half-gallon beverage jug (oh, this is Instructables, so go collect some old plastic bags and make one). Clearish is preferable.
Buy a box of Red Rose black tea. It costs more but tastes better than anything else you can get in the US (unless you like *ugh* flavored ice tea*). The Canadian variety of Red Rose is supposedly even better. And there's a prize in every box.
(*yes, I did grow up in the Deep South, where we drank ice tea, never "iced" tea).
Step 1: Tie One On
Take 5 standard size Red Rose tea bags, sort them with the tabs at one end, and tie an overhand knot in the strings.
Place bags in the water filled container and put the lid on. I like to tuck the logo tabs outside the container to keep things neat and make it easy to grab the bags for tossing into my compost bucket.
Step 2: Cook
You'll recognize when the tea is ready because it'll take on a nice tea color.
The great thing about this method is that you don't have to chill the tea - when it's done it's cold and ready to drink. I keep two jugs going so that when I empty one, I have another brewed and chilled in reserve.
This method works best for unsweetened tea or for those Pinkie users among us (aka, Sweet and Low). If you like Southern style sweet tea, there's probably an Instructable around for dissolving sugar in cold liquids.
Step 3: Salmonella
One home remedy for salmonella is drinking lots of tea. That must be why I've never gotten sick from this method of making ice tea over the last decade. Usual disclaimers.
If you do wind up in hospital, you can take all the Red Rose figurines you've collected with you to play with while you recover.
And since Red Rose periodically changes the figurines, you can look on the box and tell if the grocer is trying to fob old stock on you.