So, you're a freshly dinged level 90. What are your first steps? The first thing you ought to do before setting foot in a dungeon is head over to the Thunder Isle and introduce yourself to the Shado-Pan Assault. They will sell you an ilvl 522 neck at neutral, and as we'll get to, they're where you want to try to spend your Valor Points. You'll also want to make sure you meet the Kirin Tor Offensive or the Sunreavers, as you can earn bonus reputation for them.
Getting to item Level 435
This is the first major hurdle that players need to reach, in order to get into heroic dungeons. It was lowered from 440 to make the item level more attainable very early on in the expansion, and there are a few ways of getting to it.
The first, but perhaps not the most efficient, way is by questing. If you're patient enough to finish questlines like the Klaxxi one, you can get your hands on a 489 ring, and other items in between, but that's only a few pieces per questline, and it's not going to help you much if you're wearing all 377 gear apart from that.
While this definitely wasn't the case early in the expansion, it's now possible to lay your hands on quite a bit of crafted gear that's item level 450, and on the auction house on the servers I play on for around 200-400 gold per item. This is a great start, but can be less useful if there's no much of the gear you need on the Auction House. If that doesn't push you over the 435 item level for heroic dungeons, your next stop is Adventurer's Gear. This is sold by several NPCs around Pandaria, but Supplier Xin and Len At Arms are the two who sell 408 gear.
As an aside, if you're taking a low-geared Cataclysm alt into Pandaria, picking up the gear from these NPCs as you go can be a boon to leveling speed. There's a complete list of the NPCs in Wowhead's comments.
Killing Pandaria rares can also be a smart move, as many of them drop decent items such as ilvl 420 weapons and ilvl 440 legs. You should also be sure to run Arena of Annihilation, as it drops an ilvl 450 weapon, but choose wisely, as, while it's guaranteed, you only get one chance at it -- it's a quest reward.
Speaking of scenarios, these can be a good way to gather loot, although, as it drops randomly from reward bags, it's harder to be sure that you'll get what you need rather than getting duplicates of things you already have at a good ilvl.
Getting to item Level 460-470
This area is your next target, I've bundled them into one heading as both can be achieved by healers and DPS through the same methods. Once you've got the item level 435 that you require for heroics, clearly your best bet is to be running them repeatedly. There are various other ways to supplement your item level, but right now, especially for healers, the very fastest way to get from 435 to that 460 you need for the Raid Finder is to get your Justice Points from heroic dungeons, convert them into honor points, and use that honor to buy ilvl 476 PvP gear. Just in case you missed the memo, PvP gear now has PvE stats on it, and is therefore just fine and dandy for PvE, unless you're a tank.
For tanks, unfortunately, the PvP gear isn't so good. There are no defensive stats on it whatsoever, such as our usual dodge and parry, but gear seems to be available with stats which, while not traditionally tanky, might serve tanks well. For example, there's gear with mastery and haste on it, with mastery and expertise on it, some with hit and mastery, and depending on what tanking class you play, this might be viable.
You'll also, of course, earn ilvl 463 drops in dungeons, which will help to boost your ilvl, and you can earn reputation from these dungeons once a day, as well as valor points. Reputation-wise, the Kirin Tor Offensive sell cloaks and rings at ilvl 496, for small sums of valor at Revered, and ilvl 476 belts for gold at Honored. Given that they are the only faction from which you can purchase gear for gold rather than valor, they're a good choice for your bonus reputation. However, if dungeons and scenarios are all you do, it'll take you a while to get to Honored, so completing the one-off solo scenarios is a smart move, too, as well as some dailies. Your first valor purchase should be the ilvl 522 neck from the Shado-Pan Assault.
Of course scenarios also offer rewards, but as mentioned, they're not very predictable. They do, though, still offer valor, as well as a lower 200 bonus reputation for the first of the day. Queue times are far shorter, too, so these may be a better choice for DPS, but you get less Justice to convert and spend on guaranteed 476 gear.
After that, the Operation Shieldwall or Dominance Offensive dailies would be a smart move, as the gear they reward is ilvl 496, as opposed to ilvl 489 from the 5.0 factions, and what's more, it's not gated behind the completion of one reputation -- it stands alone. These guys sell gear for valor, not gold, though, but unless you're farming up huge numbers of Shan'ze ritual stones, you'll not be getting rep with the Shado-Pan Assault until ilvl 480.
Getting to item Level 480+
Doing dailies also awards Lesser Charms, which, alas can no longer be converted into Elder Charms of Good Fortune, used on bonus rolls in the ilvl 460-470 raid finders. Killing Thunder Isle rares is a smart move, as they have a chance to drop several useful things for the alt-gearer. Key to the Palace of Lei Shen allows you to go into the Trove of the Thunder King scenario, and they also drop items which boost your reputation with various factions. That scenario, as well as general work around the island, will award you Elder Charms.
The very second you hit ilvl 460, start doing Raid Finder, and use your bonus rolls from the farmed Elder Charms on bosses that drop gear you need to replace your lowest ilvl items. Your Lesser Charms should be converted into Mogu Runes of Fate, for use in the ilvl 480 Raid finder.
Once you're at 470, if you're tight on time, prioritize the latter two raid finders, so Heart of Fear and Terrace of Endless fights... um... I mean Spring. They award higher item level gear, so check out what you're missing and consult the loot tables for bosses. Fight smart!
Continuing our above theme, for DPS and healers, and tanks to a lesser extent, getting to ilvl 480 can also be helped greatly with Conquest Point gear, which is ilvl 493. To get from 470 to 480, it's basically more of the same. Dailies, PvP, farm rares dungeons for honor if there's any more helpful gear ther to be had. Do try your best to hold on to at least some valor points, especially as you get close to 480, because the best place to spend them is with the Shado-Pan Assault. They have rings, trinkets and bracers available at Friendly, backs, hands and legs at Honored, waist and chest available at Revered, and shoulders available at Exalted. All these are ilvl 522.
What's more, there is a lot of crafted gear available, but do note you're going to be spending a lot of money on anything useful for getting over 480, simply thanks to material costs. But keep an eye on the auction house if you're desperate!
Once you've attained item level 480, you're home and dry, almost. Get into the Throne of Thunder Raid Finder, use your Mogu Runes of Fate, spend your valor with the Shado-Pan Assault. Enjoy!
Visit the WoW Rookie Guide for links to everything you need to get started as a new player, from how to control your character and camera angles when you're just starting out, to learning how to tank, getting up to speed for heroics and even how to win Tol Barad.