Translation:I put a spoon of sugar in the lemonade.
The speaker DEFINITELY says UNA. I listened several times and that's what she says. But she is WRONG. It helps to know that the article must agree withe noun, so if you know the word is masculine, but you hear "una", then it's safe to assume that the word is wrong (or pronounced incorrectly). There are exceptions, such as "la mano" (the hand), but they are few.
a "spoon for sugar" would be a "cucchiaino da zucchero". The n in cucchiaino isn't a typo, it's a diminutive. It' necessary because cucchiaio is a tablespoon, whereas cucchiaino (small spoon) can address to a teaspoon (cucchiaino da tè), a coffee spoon (cucchiaino da caffè), an icecream spoon (cucchiaino da gelato) or the aforementioned spoon for sugar. I hope I didn't forget any.