Welcome to my Skarner guide. This build is essentially a 3-phase item guide.
1: We give him regen to increase his early game power and start on the two key core items for this build.
2: Build up his survivability so he can initiate and deal sustained dps. A: Skarner is not a burster, B: Skarner is melee, so he needs that survivability!
3: Round off his endgame damage output by completing your two key small tier items. It turns out both of these can end up granting you a lot of attack damage OR ability power. Choose depending on team compositions and item picks.

Runes:
I take scaling defensive runes to make him a great iniator at all game stages. Movement speed is great for sticking on to targets, allowing you to keep up auto-attacks for his passive, letting you spam more aoe slows. Attack speed runes are for more cdr with his passive when enemies turn around to fight.
The Quintessences and Marks may easily be interchanged for either penetration runes if you like, but my set-up allows for more variety with you dps item picks since these runes don't specifically boost AD or AP dps. If you find your playstle is suited to dancing around and using his skills, Magic Pen will help you here. If you want to get in the fray and constantly auto-attack that retreating Soraka, Armor pen will benefit you greatly. However, don't forget Skarner is still a hybrid so Penetration can only boost one end of your damage.

Masteries/Spells:
Since we gain a lot of defense through runes and items, it is best to go with 21 offense since it boosts both damage types and Skarner is a hybrid damage dealer. I personally suggest taking a combination amongst Exhaust/Ignite/Flash/Ghost, so take what masteries are suitable for your choice of spells. If you don't take Exhaust or Ignite, take 1 Deadliness and 1 Offensive Mastery to replace them. For defense take 3 Resistance/3 Hardiness in tier 1 and Strength of Spirit in tier 2; we are getting tons of mana with this build so SoS actually helps.

Stage 1:
Rush an early philo stone to get more regen for easier laning. The gold/5 is also quite excellent. After level 1 boots, grab Tear of the Goddess to build up your mana pool. We follow up with buying Sheen for the best early damage output item since Skarner has low cooldown abilities.
Stage 2:
Time to get tanky. Get Treads(probably always) or Tabis if the situation calls for it(Dem trolls like to auto lock Caitlyn, Yi and Jax somtimes you know..)
Force of Nature + Frozen Heart give you both defensive stats. More movement speed with FoN, more mana with FH - everything we want here. Spirit Visage will boost the healing from your Fracture skill and the hp regen from your FoN.
Stage 3:
Time to finish off your damage output. Late game even the dps is probably toting 2.2k health so you gotta counter their non-damage slots with some non-tanky slots of your own. Go with what your team needs damage-wise. AD Skarners will take Manamune and Trinity Force, while AP will go with Archangel's Staff and Lich Bane. The huge mana pool you've built from FH and Tear are there for a reason. :) If you're doing exceptionally well and have no problems surviving, feel free to build one of these damage items in the mix of stage 2. I usually find myself grabbing Manamune since it's 1115 gold and the passive builds your pool up a lot quicker. Stragth of Spirit for the win guys. :D

Max out Q for your slow so your partner can stick on to your focus target. Even if you took a solo lane this is still probably your best bet to max first. The given skill order(R->Q->W->E) is assuming you are doing decent and maximizes dps. If you need more survivability, swap points of your W with E instead(R->Q->E->W), taking the one point in W at level 4 for chasing and escapes.

Hope that helped for people who played Skarner, realizing he was decent, but just didn't know how to build him.
In summary:
-Lots of mana = lots of ad/ap through upgraded Tear items and more regen from Strength of Spirit. AKA more offense AND defense fo our Scorpion. ^^
-Sheen+Tear = Damage flexibility. Go ap or ad, your masteries boosted both anyways.
-Skarner ult = Ultra fun. You built tanky items, so pull those Yis out of the turrets! Sit there and attack Tryn for 3 seconds of his ult and ignite ult him! So much lulz to be had here. :D

Good luck fellow Vanguards.