To make a good cup of tea, you need boiling water and tea.
First, the boiling water. You can boil water in a pan on the stove, a kettle on the stove, or an electric kettle. All will work just fine. I use an electric kettle (cost about $25) because it is more energy efficient than a pan or kettle on the stove, it heats the water faster and I can keep it on the counter near the sink, so no carrying a heavy kettle from sink to stove. But the main thing is to get your water boiling.
Second, the tea. In the US, not everything called "tea" contains actual tea. There are an awful lot of herbal teas, or tisanes (to use the correct term) out there on the supermarket shelves. If you aren't looking for caffeine and you don't like the taste of real tea, do explore all the herbal and fruit flavored infusions out there. Real tea breaks down into two main categories, black teas and green teas. Green teas have a milder flavor and less caffeine. Both come regular or with other flavors added. Earl Grey tea has oil of bergomot, which is a citrus flavor. You can buy tea loose or in bags. To start with, I'd get the tea bags, as it is a simpler process.
I'd start by finding a plain green tea and a plain black tea--buy the smallest amount that you can of each. The main brands of black tea in the US are Lipton (which some people find very strong), Red Rose (my personal favorite) and Salada.
Then experiment. Get your mug or cup ready, and boil some water. Put the tea bag in the mug. Pour the boiling water over the tea bag until the mug is full. For starters, I'd let the tea steep (that's the official word for "sit in hot water") for three minutes. The longer you steep the tea, the stronger the flavor and, up to a point, the more caffeine you will get. Most people find that somewhere between 3 and 5 minutes gets them a good cup of tea. (I'm basing this on a standard coffee mug, say about 10-12 ounces. If you are using a tiny tea cup, reduce the time a bit.)
Then sip the tea, letting it cool off to a comfortable point first. Then try a drop or two of milk and if you like, a bit of sugar. It's now up to you how you fix your tea--I drink mine with no milk or sugar, my sister has a tiny bit of sugar and a lot of milk, a good friend uses sugar and lemon. Just like coffee, everyone has their own preference. If your grandmother's iced tea is very sweet, you might prefer a lot of sugar in yours.
If you find you really don't like the taste of tea, try herbal teas. There are fruit flavors, mint flavors and herbal flavors. Pick a flavor you like and experiment.
Do read whatever's on the box the tea comes in. Frequently you will find suggested steeping times, or they will tell you that this particular tea is good with lemon, say, instead of milk. And there may be instructions on how to make iced tea (I don't drink iced tea, so I can't help you there).