Learn Turkish: Saçı çok güzel. - Her hair is very beautiful.

The buffer s is only used when the root noun ends in a vowel (like arabası for his car). Since saç ends in the consonant ç, we just add the vowel suffix directly. Following 4-way vowel harmony, the a in saç dictates that we use ı.

Where is the word for 'her' in this sentence?

The word for her or his is onun, but it is often dropped in Turkish. The suffix -ı on saçı already shows that the hair belongs to a third person, making the pronoun completely optional.

Could this sentence also mean 'His hair is very beautiful'?

Yes! Turkish third-person pronouns and suffixes do not indicate gender. Depending on who you are talking about, Saçı çok güzel could mean his hair, her hair, or even its hair.

Why isn't there a word for 'is' at the end of the sentence?

In everyday Turkish, the 'to be' suffix for the third person (like -dir or -tir meaning is) is usually left off when making a simple descriptive statement. Just saying çok güzel is perfectly complete on its own.