(Please note that the recommendations below are largely made for in-game play. A Greninja in a competitive environment will likely make use of different moves to accommodate for smarter, more adaptive opponents. If you have any move recommendations, feel free to add them in the comments.)
The final evolution of one of three potential starters, Greninja is a powerful pokémon indeed - though perhaps not the best water-type starter ever to grace the series. Something of a speedy glass cannon, Greninja will serve you well throughout the game... so long as you make sure it always goes first.
Type: Water / Dark
Greninja begins life as Froakie, which, in most cases, you'll receive at level five. Level Froakie to 16 and it will evolve into Frogadier; get Frogadier up to level 36 and it will evolve into Greninja. Note that this evolutionary line only becomes part dark-type upon evolving to Greninja.
Dark, Fire, Ghost, Ice, Steel, Water. Immune to Psychic.
Bug, Electric, Fairy, Fighting, Grass.
As mentioned above, Greninja is largely a glass cannon sweeper. Its base defenses are average for a starter pokémon, but they typically aren't enough to ward off a super effective attack from a strong pokémon of an equivalent level. Unless you're fighting wild pokémon that are well below your level - or unelss you've taken your EV training in a radically defense-minded direction, which I don't recommend - Greninja shouldn't get hit.
Fortunately, Greninja doesn't have to get hit. Its statistical strengths all complement each other: its Attack is high, its Special Attack is even higher, and its Speed is top-tier. Give your Greninja the right moves and it will prove to be a highly-effective sweeper against a large number of pokémon, most of which won't have the opportunity to hit first.
Torrent: If your pokémon has less than one-third of its HP remaining, its water-type moves will increase in power by half. This is an excellent ability on pokémon with more HP and greater defenses. On Greninja... well, there are builds in which Torrent can effectively come into play, but the average frog shinobi won't want to get hit or lose any HP in the first place.
Protean: Your pokemon's type will change to match the move it used last. In short, Greninja becomes part Kecleon. This is an excellent hidden ability if you manage to snag a Greninja with it equipped, as you can manipulate Greninja's type freely with a variety of different moves and ensure STAB damage, but as far as I know Protean is only available if you manage to catch a Froakie, Frogadier, or Greninja via Friend Safari.
Greninja can be an extremely potent pokémon. The fact that it naturally learns Night Slash (albeit at a rather high level - you're better off going to a Madam Reminder and sacrificing a Heart Scale rather than waiting) is a big plus, and Water Shuriken, though unpredictable, is also potent if you get lucky. Nevertheless, Greninja's ideal repertoire is better served drawing on its higher Special Attack, which means looking to TMs and HMs. Dark Pulse and Surf will be your primary weapons, potentially backed up with powerhouse moves like Ice Beam, Hyper Beam and Extrasensory... or, if you like to take a chance on facing light pokémon, Grass Knot.
Should Greninja only serve as a glass cannon? Probably not. Sweepers get bad luck at times, and Greninja's power is nicely complemented by the naturally-learned Double Team. Toss in Toxic with Double Team and Spikes and you can make a decent staller (as well as a stand-up ninja), though I'd recommend taking better advantage of Greninja's straightforward offensive capabilities instead. The same goes for Mat Block, Greninja's signature move: unless you've deployed Greninja in a double battle, it's just not that useful. You're better off going for a quick kill.
EV / Super Training
Unless you want an unholy speed demon, which you're probably going to get anyway, you're better off training Greninja's offensive stats. Pick either Attack or Special Attack (I prefer Special Attack since Surf is such a fantastic move, and you'll need something with Surf to beat the game anyway) and train the heck out of it. You can boost Greninja's defenses a little bit if you want to take advantage of Torrent, but so long as you choose your battles wisely Torrent isn't that necessary.
Catching a Greninja
Catching a Greninja usually requires catching a Froakie first. The only ways of doing so beyond the Friend Safari or straight-up trading with someone are to choose Froakie as your starter, or to choose Chespin as your starter. In the latter case, Shauna will give you a Froakie upon completing the game for the first time.
Wobble on October 30, 2013:
I like to use mixed Greninja, albeit casually. Water Pulse/Surf is for STAB and WP can give the occasional confusion, Aerial Ace can cover 3 of its weaknesses (Bug, Fighting, Grass). Those are the main two moves I would recommend.