There were a lot of things all at once there.
@medivah, go ahead and check out pillar's link. It's short, but it's mostly to the point. Gunpowder happened in china long before Europe, and it didn't really come into popular use there until the late middle ages. As for who invented it, we don't really know. It came from a bunch of people independently. We do know for sure, though, that it wasn't just one guy. Additionally, guns didn't start as 'guns'. they started as cannons, primarily. There were smaller arms (i.e. hand cannons) but more modern individual firearms didn't come into use until much later.
@Passerby: I do indeed know about the Armenian Genocide; while I haven't really played around with the Ottoman empire in a while, I have touched on it in the past. I'm not sure whether that was an attempt to call me out for not knowing something important or what, but if you DID have a question, You'll need to be a little more specific than the name of the event.
Finally, @Mayhem Death. That question was almost big enough to garner itself a full blown blog post, but to be fair, it's pretty simple if you avoid the long, complicated genealogy and royal family dealings.
There were 3 big guys that affected Persia, and made it as big as they were. That would be (as Orange Kun suggested) Cyrus the Great, Darius I (sometimes referred to as Darius the Great) and Xerxes. Cliff's notes:
Cyrus the great was really the reason why the other rulers were so successful. He laid a brilliant foundation for the empire. Essentially, he established a national capital in Pasargadae, and ruled the entire empire centrally. The Persian empire is generally regarded as the most stunning example of central administration in ancient times; it was truly advanced.
Darius was responsible for the first invasion of Greece. They did manage to get some territory, and in fact, the empire was at its largest under Darius. However, after a stunning loss at the battle of Marathon (quite famous in ancient Greek history; it's where we get the term 'Marathon' today), they were turned back.
Xerxes was responsible for the second Greek invasion, where instead of coming over by sea (their massive mistake the in the first war) they came over land, in the north, and swept down into Greece. Long story short: they lost there, too. Oh, and the movie 300 was based off of the battle of Thermopylae, one of the famous battles here.
But the actual answer to the question, 'how did they get so big', is really boring in it's simplest form: they conquered stuff. They essentially integrated cultures and other peoples into the empire over time, some of them peacefully, and some of them not so much. They were largely regarded as successful because of how excellent their centralized administration was. For instance, The Persian empire is where we see the first 'official state language' in the history of the world. They allowed provinces to have other dialects, but all business that was official was all done in a specifically chosen dialect (Old Persian, if I'm not mistaken).
Additionally, they were also quite unique for their religious integration. While places like Greece all generally followed the same basic religion, there were tons of cults, different focuses on different gods by location; it was unorganized. In Persia, with King Artaxerxes (who came right after Xerxes... easy to remember, as it turns out) enforced Zoroastrianism as a state religion, and that was the end of it. I'm not sure if that was the first instance of enforced state religion (as I wrack my brain for previous instances) but I do believe it was. Other civilizations had universal religions, but there was a lot of variance by geography; that wasn't the case here.
So, essentially, The Persians were successful because of their awesome centralized government, their stunning integration of border states (through peaceful measures or otherwise) and later, the religious integration.
