Learn Turkish: Diğer kitabı okuyorum. - I am reading the other book.

There are two things happening here! First, because you are reading a specific book ("the other book"), it takes the specific direct object ending (the accusative case), which is -ı in this word. Second, when you add a vowel suffix to a Turkish word ending in p, that letter usually softens into a b. So, kitap + ı becomes kitabı.

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

Turkish doesn't have a separate word for "the". Instead, when a direct object in a sentence is specific (like the book, rather than a book), Turkish adds a suffix to the noun to show this. The -ı at the end of kitabı does the job of "the" here.

How is the verb okuyorum put together?

It breaks down into three simple parts: oku is the root of the verb (read), yor is the present continuous tense suffix (like "-ing" in English, showing the action is happening right now), and um is the personal ending that means "I". Combined, they mean "I am reading".

Where is the word for "I"?

In Turkish, you don't usually need to say the word for "I" (ben) because the verb already tells us who is doing the action. The -um ending on okuyorum makes it perfectly clear that "I" am the one reading!