"Would" is a very confusing word in English. It can mean opposite things, but native English speakers don't usually notice how confusing it is.
"Would you?" can be a polite way of asking asking a question. "Would you like some coffee?" is basically the same as "Do you want some coffee?" but a little gentler. It implies more permission to say no.
You say yes to a "would you" question by saying "I would," or, "yes, I would."
EXCEPT
"I would" can also be a polite way of saying no. It means that the answer would be yes under some different circumstance. Someone might say "I would have some coffee, but I'm avoiding caffeine." This is like saying, "Under a different circumstance I'd gladly accept your offer."
So if I ask "would you like some coffee?" and you say "I would." That means yes. If you say "I would, but I just had some." That means no.
Many English learners find this extremely confusing, for good reason.
Fiddlestick is genius. If my neighbor came out her front door and called "Fiddlestick!" and that cat came trotting out of the bushes, I would fall over and die.