The verbs we use for tea and coffee are the same.
You can "make" some coffee or "make" some tea. Or, if you want to use a more specialized word, you can "brew" either coffee or tea. For coffee, this normally assumes you have a coffee maker. For tea, of course, you can "brew" tea by "warming up" water in a kettle and "steeping" the tea in the hot water.
If you are in a rush, you can "make" some instant coffee. Or you can "microwave" (verb) coffee using special coffee filters. For tea, you can "microwave" some water and then add a tea bag to the resulting hot water, and let the tea (bag) "steep" in the hot water. This is great for quick preparation, but I wouldn't "prepare" coffee or tea using a microwave for anyone but myself, a roommate or a friend (i.e., not for a large party or a dinner party).
You can "make" (or "brew") some "sun tea" by letting the tea bags "steep" in a large jar of boiled water, which you set out in the sun.
All these are different ways to "make" or "prepare" tea and coffee.
Then you just "drink" the tea. Although you probably want to "sip" the tea while it is still very hot. In American English we rarely say will you "take" some tea, although will you "have" some tea is okay; but more common is do you "want" some tea.
In the US, people "drink" iced tea (or: ice tea) all the time. And in some places in the USA, people "take" or "drink" coffee iced. That is, they "drink" iced coffee.
In American English it's common to start that kind of response with "It's funny, [...]". For example, if someone told you they found a hundred dollars on the street last week, you might say, "It's funny, me too!" A few other ways of opening stories are "This one time, ..." or "I remember this once, ..." These are all very colloquial examples but seem appropriate for the situation you described.
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When you think about pleasant memories, you can describe it as reminiscing.
You can refer to the memories as reminiscences or, if you really want to lay it on thick, sweet reminiscences.
These expressions are regarded as quite old-fashioned, but I think the whole concept is quite old-fashioned. I can't imagine a sk8er boy doing it.