Learn Turkish: Kuş uçuyor. - The bird is flying.

This happens because of 4-way vowel harmony. The root of the verb is uç- (to fly). Since the vowel in the root is 'u', the present continuous suffix changes to match it, becoming -uyor.

Why isn't there an extra personal ending after uçuyor?

In Turkish, the third-person singular (he, she, or it) doesn't take a personal suffix in the present continuous tense. The word kuş (bird) acts as an 'it', so just adding the tense suffix -uyor to the verb root is all you need.

How do we know it means 'the bird' when there is no word for 'the'?

Turkish doesn't have a definite article like 'the'. The single word kuş can mean 'bird', 'a bird', or 'the bird'. Because it is the subject performing a specific action right now, 'the bird' is the most natural translation in English.