Ultimately, our knowledge of ancient cultures is generally shaped by the combination of archaeological evidence and the literature they left behind. The Epic of Gilgamesh, for example, is an invaluable source of insight into Ancient Mesopotamian attitudes toward death. When Enkidu lies dying, for example, he reports a vision of the Underworld, from which modern-day readers can infer much of what ancient Sumerians imagined the afterlife entailed. In addition, one might note Gilgamesh's complete failure to overcome his immortality, despite his own status as two-thirds divine. The message in Gilgamesh is then clear: the status of immortality belongs only to the gods, while death is inevitable for all human beings.
In the case of Ancient Egypt, perhaps the most valuable source of textual evidence can be found in the Book of the Dead, a collection of funerary poems, prayers, rituals, and so on. To gather knowledge on Ancient Hinduism, the most important source would be the Vedas, a vast collection of works that comprises the religion's oldest, most important, and most foundational texts.
In addition, to the textual works, one might also look to archeological records. This would be an especially powerful source of insight in the case of the ancient Egyptians, who are famous for their royal tombs and the practice of mummification (traditions that speak volumes about this ancient culture's attitudes and beliefs about the dead). Similarly, there are burial grounds for the ancient Mesopotamians as well, as can be seen with the Royal Cemetery of Ur.
What is noteworthy about Ancient Hinduism, and what differentiates it from the other two cultures addressed in this question, is that Hinduism is still a living religious tradition. Certainly, you can expect it to have evolved and changed from its ancient form, but even so, observing and learning about Hinduism as it is practiced today can give rich insight into the overall tradition stretching all the way back throughout its history. The reincarnation of the soul, the concept of brahman as a transcending universal force, ideas of karma and dharma—all of these represent pillars of traditional Indian culture, and that culture remains vibrant and alive today.