I think that one has to embrace a rather open perspective in understanding the roots of Hinduism. It's difficult because the religion itself is quite old. Its roots can be traced back to a couple thousands of years B.C.E. This makes its roots very difficult to fully ascertain. I might suggest that one way that a person can begin to understand some of the basic roots within Hinduism is to begin the process of examining why some of the rituals done today have been done in the past. Assessing why some of those elements are practiced today and understood in both modern contexts and the context of the past can help individuals gain greater insight into the religion's roots and relevance. For example, why is Diwali celebrated? Why is the Ganges River so revered? These are just two examples of how modern practices can reveal a great deal of insight into the roots of the religion and its practice. Essentially, I think that the roots of the religion are so far embedded in human historical experience that one might be best set to understand why the constructs of the religion today are there, their meaning, and how important these constructions have been in the development of the religion. In this method of "working backwards," one might be able to gain greater understanding about its roots.
As rightly said in the answer above, Hinduism originated thousands of years ago and there are no authentic information about that early period to be able to know with clarity and certainty when, how, and where Hinduism began to take rots and how it developed during early period of its existence.
The most extensive and clear information we have about Hinduism are some texts like Vedas, Mahabharata, and Ramayana, which are thousands of years old but still no where near as old as the Hinduism. Still these books do contain description of times and events that may have been much closer to the beginning of the practices that developed into Hindu religion. For example these books talk about a period when river Saraswati was still flowing, and of submerging of the port town of Dwaraka under the rising sea level. We know now that drying up of Saraswati and submerging of Dwaraka happened more than ten thousand years back. Therefore, we can use the information contained in these texts to get a scrappy picture of some aspects of development of Hinduism.
I would like to divide Hinduism in two clearly distinct part. One is the social code of conduct for the people in the society. The second is the philosophical concepts which form the basis for justifying and promoting some of the practices prescribed in Hinduism.
I believe both the social code of conduct and the philosophical underpinnings developed more than ten thousand years back. There must have been some form of social system in existence but prior to founding of Hinduism. But this may not have been very extensive in terms of either aspects covered or the people following it. The some leader of people or a King, identified by the name Manu, and described as father of entire civilized mankind, improved upon, and formalized this code and enforced it among his followers more effectively.
As Manu is called the father of entire civilized mankind, I believe this event must have taken place somewhere in the early stages of the concerned people taking up a settled life of people engaged in cattle breeding and farming, giving up the earlier life of a hunting and gathering nomad living in forests. The system or the movemets stared was carried on, perhaps with improvements by subsequent heads of those people . These subsequent heads, who may or may not have inherited the position based on their birth.
The social system formulated by the first Manu coverd the philosophical underpinnings also which were developed by others before him and were already well known among scholars. One of the important aspect of these philosophical concepts was the "Theory of Sankhya" developed by "Kapil Rishi".
This system developed and implemented by various Manus was entirely created, preserved and used base on verbal communication. Most probably there was no viable written communication system at that time. So we do not know exactly what the content of this system was. An old Hindu text called "Manusmriti" which is supposed to be compilation of the Manus edicts was written just about 2500 years back, and cannot be considered to be a reliable record of the original system. But we can guess a few things about this system.
The most important part of the system is what I call a "Knowledge management System". This system was specifically designed to preserve, convey and use knowledge effectively using verbal communication system. One important part of this system was development and standardization of language, which was called "Sanskrit" meaning "refined" Language. This Knowledge management system played a very important role in development of the entire Indian Subcontinent Civilization by making knowledge available to people easily. For this reason I have named this civilization as "Sanskrit based Civilization"
Manu also introduced a system of division of labor which also played an important role in the The Knowledge Management in particular, and of success of the Sanskrit Based Civilizaion in General
So, According to me this is the story of root of Hinduism. I have already made out a long answer, and I do not want to stretch it very much further. I will only say that there have been many changes in the practice of Hinduism - including creeping in of bad practices and many backlashes against them - since the original development of the code given by Manu. In most likelihood the Hinduism as practiced today must be very different from as prescribed by Manu.