Locate the infinitive and determine how it is used.

A good book to read is Great Expectations.

I know the infinitive is to read, but I don't get how to find out its use.

Possible answers are:

1.) Noun

2.) adjective

3.) adverb

I agree with the previous answer. It surely an adjective. Remember that an adjective is a word that modifies a noun or pronoun and answers the questions: which one? what kind? and how many? An infinitive that acts like an adjective will do the same thing.

Example: After breaking his leg, Dave had many obstacles to overcome.

To overcome is the infinitive and tells which obstacles have to be overcome. Thus, it modifies the noun, obstacles.

In you case it modifies the noun, a book.

The infinitive in the sentence is to read, as you have already written.

It is used in this sentence is 2. adjective.

You are describing the book - what kind of book is it? A (good) book to read.