The basics of leveling advice is still the same... if this is an alt get it as many heirlooms as you can swing for the XP boost and to avoid having to think about gear upgrades (although it is kind of a bummer when a really nice piece of gear drops and you don't have any use for it because you're using an heirloom, but no gift without price, right?) and if you can, run the instances, especially if you don't have heirlooms. Back when the general revamp to instances went live, a lot of gear that was just kind of 'meh' for shamans got changed to actual be decent. Examples include the Deathchill Armor from Razorfen which is a decent piece for a resto shaman at that level or the Gahz'rilla Scale Armor from ZF.
I know that instances can be hard to get groups for when you're leveling nowadays. I have hopes that the new cross-realm LFG system will help alleviate this to some extent, and running instances (especially ones that you can gather a whole lot of quests for, like Uldaman, Zul'Farrak, the Temple of Atal'Hakkar and Blackrock Depths) can really help you tighten up what you're expected to do in an instance as you progress in levels. Another way to 'stress test' yourself as well as get XP is in the Battlegrounds, especially now that XP gain is allowed there. If you lack the patience to wait for LFG, just don't want to run the same instance over and over again but are perfectly willing to kill the same Alliance/Horde players time in and time out, or want to see what a raid interface looks like (since most BG's use one) then BG leveling is definitely a strong option.
Once you hit Outland, instances become an even more tempting way to get some decent gear if you can arrange it. Also, although it's not as much fun as running a full group, do not be afraid to accept when a bored level 80 guildmate offers to run you through the entirety of Coilfang Reservoir. People will tell you that this isn't really in the spirit of things, and they're right, but until that new LFG functionality arrives let us be honest among each other: getting lower level instance runs is harder now. You can still get decent XP and some nice gear in an afternoon of your Ulduar/TotC geared buddy showing off just how much damage Blizzard does, so don't close your mind to the option. When I run a lowbie friend or friend's alt through an instance, I try and get as many of them as I can in to spread out the gear drops, but you'll figure out how it best works for you. If you have a lot of lowbie friends, you can always try and run the instance the way it was meant to be run.
If all else fails and you hate instances and BG's, there's always the tried and true questing through zones. There's actually quite a few zones available to you (our original 41-60 and Outland guides cover them in detail) and if that's the road you choose, it will absolutely work just the same as it did before. In fact, I've found that Outland in general goes pretty quickly since patch 3.0 dropped. You can easily do nothing but zone quests, and be level 64 (with rested and heirlooms, possibly 65) before you even finish up whichever zone you pick after Hellfire Peninsula. If you hit Nagrand as soon as it's available, you could very easily ding 67 or 68 by the time you're done, meaning that (if you choose to) you can skip Shadowmoon Valley, Blade's Edge Mountains and Netherstorm entirely.
Between level 41 and 68 you'll gain a few new non-talented abilities. You picked up Chain Heal at 40, and you'll be gaining Call of the Spirits at 50, your third totem bar allowing you to drop four totems at once. From there you'll get the next big totem, Wrath of Air, at level 64 (I personally love Wrath of Air and drop it very often when I'm healing) followed by the two pet totems, Earth Elemental Totem at level 66 and Fire Elemental Totem at level 68. While these are both fine totems (EE saved my butt the other day when we summoned the Headless Horseman before realizing the tank wasn't actually in the instance yet, as it proved able to tank the dude for its entire duration as long as I was fast on the heals) I've always lamented that EE Totem doesn't turn the shaman into an earth elemental for its duration. (That would be one way for Shamans to tank, if there was any desire for that.) Same with Fire Elemental Totem: it's a fine totem, it does what it is intended to do, but since neither pet totem can be controlled by the shaman you always end up watching it run over and whack some mob that hit you with a spell you didn't even notice while ten other mobs are punching you in the groin. (Assume for the same of the argument that these are short and very vindictive mobs.)
These levels are the ones where the talent trees start hitting their stride. It's possible to have spent 31 points in a talent tree by 40, which means you'll be able to pick up talents like Elemental Mastery, Dual Wield, or Cleanse Spirit. By level 68. you can easily have spent 51 or more talent points in a tree to pick up the capstone talents and even if you haven't quite, a 44/15/0 build is still that of an elemental shaman. (I pulled those talent numbers out of my buttocks for illustration purposes, please don't write in complaining that no elemental shaman would go 15 points in enhance.) It's in Outland that you'll fine the first mail really designed for elemental or restoration (if you just hate wearing leather or cloth) as well as spell power weapons and shield. (These things exist in Azeroth to be sure, but are far more common through the Dark Portal.)
This covers most of the basics for the new or newly leveling shaman, be he alt or new main. Next week, restoration spec for someone as clueless as me, written by someone as clueless as me, namely me.
Check out more strategies, tips and leveling guides for Shamans in Matthew Rossi's weekly class column: Totem Talk.