Learn Turkish: Bana göre en büyük değer aile. - To me, the greatest value is family.

The postposition göre (according to) always requires the word before it to take the dative case (the 'to' or 'for' direction). The pronoun ben (I) has an irregular dative form: it changes its root vowel and becomes bana (to me).

Does bana göre mean 'compared to me' or 'according to me' here?

Here it means 'according to me' or 'in my opinion'. While göre can also mean 'compared to' (as in 'He is tall compared to me'), you are stating a personal belief in this sentence, so the 'according to' meaning is used.

How do we form 'the greatest' using en büyük?

The word büyük means 'big' or 'great'. Placing the word en (the most) before any adjective creates its superlative form. So en büyük translates directly to 'the biggest' or 'the greatest'.

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

In Turkish, the verb 'to be' (is/am/are) usually shows up as a personal suffix on the final word. However, for 'is' (third-person singular), the formal suffix -dir is very often dropped in everyday language. Because of this, the sentence just ends with aile (family) but is understood as 'is family'.