Learn Turkish: Ablan çok yorgun. - Your older sister is very tired.

In Turkish, possession is usually shown by adding suffixes to the end of the noun. Here, the root noun is abla (older sister). Because it ends in a vowel, we just add the 2nd person singular possessive suffix -n to make ablan, which means "your older sister".

How would I change this sentence to say "My older sister is very tired"?

To say "my", you use the 1st person singular possessive suffix. Since abla ends in a vowel, you just add -m instead of -n. The sentence becomes Ablam çok yorgun.

Where is the word for "is" in this sentence?

There isn't a separate word for "is"! In Turkish, "to be" (am/is/are) is often expressed through suffixes at the end of the sentence. For third-person subjects like "your older sister" (she), no suffix is needed at all. The sentence literally reads as "Your older sister very tired," but the "is" is naturally understood by the grammar.

Does abla mean any sister, or just an older one?

It specifically means older sister. Turkish has distinct words for older and younger siblings. If you wanted to talk about your younger sister, you would use the word for younger sister, making it kız kardeşin.