If you wish to know about Indian Philosophy I recommend you begin by reading D.P. Chattopadhyaya's 'What is living and what is dead in Indian Philosophy '. This is a seminal book, and very informative.
There are two main subjects in philosophy : ontology and epistemology.
Ontology is the study of existence. In other words, the questions asked in ontology are, does God exist, does the Universe exist ( or is it Maya, an illusion), does the soul exist, do ghosts, fairies and witches exist, do unicorns exist, etc.In other words, what is really real, and what is only apparently real ?
The ontology of Nyaya philosophy, of which I am a follower, is realistic and pluralistic. It is realistic, because Nyaya philosophy believe that the world is real, and it disagrees with Vedanta philosophy which believes that in the ultimate analysis the world is unreal i.e. Maya.
Nyaya philosophy is also pluralistic. In this respect also, it is in sharp contrast to Vedanta. Vedanta philosophy is monistic. In other words, Vedanta believes that there is only one entity in the world, that is called Brahman. On the other hand, Nyaya philosophy believes that there are innumerable real entities in the world, e.g. men and women, houses, trees, tables, glasses, etc., and these can not be regarded as one, as Vedanta believes.
Epistemology is the study of the means of acquiring true knowledge. In Indian philosophy it is based on the pramanas, or means of acquiring true knowledge. There are several pramanas, e.g. pratyaksha pramana or knowledge derived from our 5 senses, anumana pramana or knowledge derived by inference e.g. where there is smoke there is fire. We may not see the fire, but infer of its existence by the smoke. There is shabda pramana, which is knowledge derived by an opinion of an expert, e.g. a doctor or physicist.
In Nyaya philosophy ( and I am talking of the original Nyaya of Gautam in his sutras, and not its subsequent theological distortions by Vatsyayana, Udayana, etc), which says that nothing is acceptable unless it is in accordance with reason and experience ( which is precisely the scientific approach ), the pradhan pramana or principal means of acquiring true knowledge is pratyaksha pramana. For example, if we ask how do we know that this tree in front of me exists, the answer is : because we can see it with our eyes, it is pratyaksha.
But much of our knowledge is also derived from anumana or inference. For example, Rutherford propounded his theory of the atom consisting of a central nucleus ( of protons,neutrons,etc) and electrons orbiting it ( like the planets orbiting the sun ) by inferring it from the scattering of alpha rays ( which are helium ions), although he never saw ( and we still cannot see ) an atom, as it is too small.
The existence of black holes has also been established by inference or anumana, although no one has actually seen a black hole, because its density is so great that light cannot escape from it, but we infer its existence from the movement of other neighbouring heavenly bodies which proves that there is a heavenly body in the neighbourhood which, though not visible, is excercising its gravitational pull so as to make the visible heavenly bodies move in the manner they do.
Shabda pramana is the knowledge we acquire from the statement of an expert. For example, we accept the truth of Einstein's equation, e=mc2, because Einstein is an eminent physicist, although we ourselves may not be able to understand how he reached to that equation. We accept the diagnosis of our medical doctor because of his reputation.
Nyaya philosophy, of which I am a follower, says that pratyaksha pramana is the pradhan praman. and other pramanas are subject to, and dependent on, pratyaksha. This is also the scientific approach, because scientific theories have to be tested by experiments, and only when they are found valid by experiment are they accepted. Thus, Einstein's general theory of relativity was only accepted after it was tested by experiment in 1919 by Eddington and his associate scientists, who noticed the bending of light coming from stars by the gravitational pull of the sun during a full solar eclipse as predicted by Einstein's theory.
However, pradhan pramana, too, may sometimes not give true knowledge. For instance, we see the sun arising from the East and setting in the West, which creates the impression that the sun goes around the earth, and this is what people believed earlier till Copernicus established that it was the earth which goes around the sun, not the other way around ( The Indian scientist,Aryabhatta had also suggested this in his book 'Aryabhatiya' in the 4th century A.D. i.e. long before Copernicus ).).
We see a mirage and think it is water, which is untrue.
So how can we be sure that pratyaksha leads to true knowledge ?
We can be sure by two ways ( 1) application of reason, and (2) experiment.
By applying reason we can understand that the appearance of the sun going around the earth could be because the earth is rotating on its axis.
By experiment, we can know the falsehood of water in the mirage, because when we approach it it disappears, and does not quench our thirst.
We presently accept the duality of things, i.e. waves can be regarded as particles ( the Quantum Theory of Max Planck ) and particles can be regarded as waves ( the Quantum Mechanics of De Broglie, Heisenberg, Schrodinger, etc) because that is what was found by experiment