First, let's examine why the Quran is the word of God. In Surah (chapter) An-Nisa, Verse 82, it is stated, "Will they not, then, try to understand this Qur'an? Had it issued from any but God, they would surely have found in it many an inner contradiction!" Additionally, in Surah Fussilat, Verse 42, it is stated, "... no falsehood can ever attain to it openly, and neither in a stealthy manner, [since it is] bestowed from on high by One who is truly wise, ever to be praised." The tafsir (commentary) on this by scholars (tafsir is needed generally for the people who don't understand Arabic) is that the Quran is free from contradiction because it is sent from God.
Next, there are many scientific proofs that exist in the Quran, revealed about 1400 years ago in a time without microscopes, telescopes, sonograms, etc. Surah 51, Verse 47, states, "And it is We Who have constructed the heaven with might, and verily, it is We Who are steadily expanding it." In Arabic, the phrase "inna lamoosi'oona" translated means "it is We Who are steadily expanding it." The prefix "la" means "to a big extent." "Heaven" is translated from "space" or "universe" in Arabic. "We," translated, is the pronoun that isn't showing plurality, but showing the honor/majesty of someone. In this case, it refers to the majesty of Allah. Scientists have confirmed the Big Bang to have occurred, and have said the universe is expanding at a great rate.
In Surah 21, Verse 104, it is stated,"That Day We will fold up heaven like folding up the pages of a book. As We originated the first creation so We will regenerate it. It is a promise binding on Us. That is what We will do." "That Day" refers to the Day of Judgment. The Big Crunch, presented by scientists, says that "...at some point in the remote future all matter in the universe will converge into an infinitely dense point in space, resembling a massive black hole. The end of the universe would then resemble its beginning-a singularity at which the laws of physics as we know them no longer apply" (Encyclopedia of Science and Religion). This refers to folding up heaven. Like at the time of the Big Bang, the universe will return to what it was, referring to "regenerate it." God says that this will undoubtedly happen.
In Surah 41, Verses 10-11, it is stated, "Then He turned to heaven when it was smoke and said to it and to the Earth, 'Come willingly or unwillingly.' They both said, 'We come willingly.'" The Arabic word "dukhaanun" means "smoke." Scientists have said the universe came from a formation of hot gas, resembling the form of smoke.
In Surah 21, Verse 30, it is stated, "Do not the unbelievers see that the heavens and the Earth were sewn together and then We unstitched them and that We made from water every living thing? So will they not believe?" The arabic word "ratq" means "blended" or "mixed in each." Before the Big Bang explosion occurred, everything was collected uniformly. Only when it occurred was everything separated. So the universe and Earth were "sewn together" as one, and the explosion "unstitched" them.
There are more proofs about the universe and the paths that the planets follow, but there are scientific miracles in other subjects of study.
Surah 24, Verse 40, states, "Or [the unbelievers' state] are like the darkness of a fathomless sea which is covered by waves above which are waves above which are clouds, layers of darkness, one upon the other. If he puts out his hand, he can scarcely see it. Those Allah gives no light to, they have no light." The sea turns dark at a depth exceeding 600 feet, known as the mesopelagic layer, and is virtually dark beyond 3,000 feet, known as the bathypelagic layer. No human could dive this deep 1400 years ago. Scientists have also confirmed "sub-surface waves", which "occur on density interfaces between layers of different densities," and can only be studied through technology which indicates temperature or salinity changes (Oceanography, A View of Earth).
In Surah 39, Verse 6, it is stated, "... He creates you stage by stage in your mothers' wombs in threefold darkness. That is Allah, your Lord. Sovereignty is His. There is no deity but Him. So what has made you deviate?" Scientists have fairly recently said the embryo is developed in three stages, which can be called the pre-embryonic stage, the embryonic stage, and the fetal stage. This was discovered through microscopes, sonograms, and other inventions that are only available in modern times.
In all honesty, there are more miracles and proofs like this in the Quran. One has to just look at the Quran itself and learn the religion from those who practice it (i.e. scholars), instead of learning it from Christians, Jews, atheists, etc. You don't learn to play basketball from a football coach. Only listen and learn from the Muslims, the people that actually know the religion, and honestly, they will be very happy to teach it to you.