Learn Turkish: Kitaplığa üç tane roman koydum. - I put three novels in the bookcase.

The suffix -lık (which follows vowel harmony) is used to create new nouns, often indicating a place or a container for something. Here, it attaches to kitap (book) to create kitaplık, which means a place for books: a bookcase or bookshelf.

Why is there a ğ in kitaplığa instead of a k?

The base word is kitaplık. Because you put the books into a destination, we need the dative suffix -a (to/into). When this vowel suffix is added, the hard k at the end of kitaplık is sandwiched between two vowels and softens into a ğ. This is known as consonant mutation.

Why is roman singular if the English translation says "three novels"?

In Turkish, whenever you use a number like üç (three) to count something, the noun that follows must remain singular. You never add the plural suffix -lar or -ler after a number.

What is the purpose of tane in this sentence? Can I skip it?

You can skip it and just say üç roman, which is perfectly correct. However, tane (meaning "item" or "piece") is very often used after numbers when counting physical objects. Including it makes your Turkish sound very natural and conversational.