Of course when one finds it necessary to know about one religion, the first books or valid references they would be offered, are each religion's number one book! (Quran, Bible, etc), but what about Hinduism, what is its number one book? Where to start?
There is no one comprehensive book in Hinduism.
You should read a low level introductory book that nevertheless gives a decent overview of Hinduism. Otherwise you will have difficulty in understanding Hindu scriptures. Books like 'The Hindu mind' by Bansi Pandit and 'The complete Idiot's guide to Hinduism' by Linda Johnsen would help. Another introductory text is 'A primer of Hinduism' by D. S. Sharma. A good text is 'Essentials of Hinduism' by Swami Bhaskarananda. A good survey of Hindu scriptures is 'Windows into the Infinite A guide to the Hindu scriptures' by Barbara Powell. An advanced level beginner text is 'The Spiritual Heritage of India' by Swami Prabhavananda. You can also read 'Hindu Gods and Goddesses' by Swami Harshananda to learn about the many Hindu Gods and Goddesses.
You can then read some of the seminal texts of Hinduism like the Gita, the Upanishads and if you are really interested in the Brahma Sutra. You can read the Gita translated by Swami Tapasyananda. You can also read ‘Universal Message of the Bhagavad Gita: An Exposition of the Gita in the light of Modern thought and Modern Needs’ by Swami Ranganathananda. If you want to go really deep into it then commentaries of Sankara on the Gita, the Upanishads and the Brahma Sutra are a must. You can read Srimad Bhagavad Gita Bhasya of Sri Sankaracharya translated by Dr. A. G. Krishna Warrier. You can also read Brahma Sutra Bhasya of Sri Sankaracharya translated by Swami Gambhirananda. Reading the translations of Upanishads by Swami Nikhilananda and Swami Gambhirananda will also be helpful.You will find many Hindu seminal texts on online sites. There is a list in one of the questions here.
You can then read the 9 volume Vivekananda's complete works if you have the time for it. If not, then I recommend 'What religion is in the words of Swami Vivekananda' edited by Swami Vidyatmananda. You can also read Patanjali's Yoga Sutra.
If you have the time for it then you can go through the entire Mahabharata which is full of gems. You can try reading K. M. Ganguli's translation of the Mahabharata. You can also read the translation of Srimad Bhagavataam by Swami Tapasyananda.
Till now you have gained theoretical knowledge. If you have the time then you can go through the Ramakrishna Kathamrita (translated as the 'The Gospel of Sri Ramakrishna) to read about an exemplar of the Hindu tradition.
You can go to any Ramakrishna Vedanta Center to learn about Hindu scripture. You can find out about the Centers at the following web site: www.vedanta.org. You will get most of these books from www.vedanta.com or from Amazon.
I have given the list that I found useful. It is definitely inclined towards Advaita. You will need to read commentaries of Hindu seminal texts by other Acharyas if you are interested in other Vedantic traditions.