Learn Turkish: Siz çok iyi yüzüyorsunuz.

It starts with the verb root yüz (swim). We add -üyor for the present continuous tense, using ü to follow the vowel harmony rules for the word yüz. Finally, we add the personal suffix -sunuz because the subject is siz (you, plural or formal).

The Turkish verb uses the present continuous tense, but the English translation says "You swim" instead of "You are swimming". Why?

In Turkish, the present continuous tense (-iyor) is frequently used to describe general facts, habits, and abilities, not just actions happening right this second. It is very common to use it to express statements like "You swim" in general.

Doesn't iyi mean "good"? Why is it translated as "well" here?

Yes, iyi is the adjective for "good". However, in Turkish, words that describe nouns (adjectives) can usually be used to describe actions (adverbs) without changing their form. Because of this, iyi works as both "good" and "well" depending on the context.

Is it necessary to use the pronoun Siz at the beginning of the sentence?

No, it is optional. The personal suffix -sunuz at the end of yüzüyorsunuz already makes it perfectly clear that the subject is "you". Including Siz just adds a little bit of extra emphasis.