I'm actually surprised this has so few answers, and not too extensive ones even...
Most Event Pokémon (Mew, Celebi, arguably Manaphy and Phione, Jirachi, Deoxys, Shaymin, Darkrai, Arceus, Keldeo, Meloetta, Genesect and 3 more since X/Y) are not obtainable in game by any means other than Trading (from someone who did get it by one of the methods detailed hereafter), Cheat devices (such as Action Replay) or glitches (such as the Tweaking glitch in D/P). The few exceptions require a side game such as Pokémon Ranger, or as I state below (via official distribution).
They are, however, being distributed occasionally by different means, usually via either Wi-Fi/Internet, Local distributions by Stores (GameStop, Walmart, hobby stores) or at special events (Pokemon Days, World Championships, ...) or Global Link. These distributions are usually live for several weeks, unless they're bound to a date (such as with Worlds distributions). This means it's usually fine to check for news on pokemon.com or fan sites once a week or even once a month (as they tend to be announced a few month in advance).
Once the distribution period is over, there is no legal way to get the event. You can only trade online to get the Pokémon someone else got there, but the event is gone for good.
Most event exclusive Pokémon are being distributed again after some time, though. The newer the Pokémon, the smaller the chances are it'll be distributed again, so if you missed an event by just a few months, you'll probably have to wait for quite a while until there is another event with it.
One last important detail is that events are usually only available for the latest main series games, which currently means X or Y. Unless you own a copy of those, you sadly won't have access to events any more.