This is my first Mobafire guide, and it is for AP Skarner. AP Skarner, as of this writing, is able to out self-heal an AP Vladimir, which is pretty awesome considering that's Vlad's whole gimmick.
The real key to AP Skarner is to buff his attack speed high enough to recharge his skills, and to increase his movement speed to both increase the effectiveness of Impale and make up for his lack of a closer. To that end I use Attack Speed Marks and Seals with Quints of Movement speed. For Glyphs I add some AP per Level to make his skills do that much more damage. Another way to build him would to replace the Glyphs with Attack Speed and put AD Marks on him to up his damage while abilities are on cooldown, but the way I do it meshes more with my play style (and the runes leftover from my regular champs).
The two most important Masteries for Skarner are Alacrity and Quickness. I also like putting a point in Haste. These combine to reduce his cooldowns via basic attacks and to make Impale as good as it can get by enhancing his movement speed. I put his final point in Offensive Mastery because AP Skarner can potentially solo top in 5's AND 3's, so the extra damage to minions helps him clear minion waves.
Skarner needs lots of mama/mana regen. This is fortunate, because when building him AP, it already makes most of your choices for you. You build Tear of the Goddess with Catalyst the Protector as your first two items in order to really maximize his mana as early as possible. This leads to a very high level of sustainability for Skarner, especially due to the massive heals he gives himself. I give him Boots of Swiftness instead of Mobility because the focus on AP Skarner isn't in Ganking, as it is with Jungle Skarner, but with utilizing Impale to the best of your abilities, and the extra speed of Boots of Swiftness means you'll pull your target that much further. For the mid-game, you upgrade the Tear into an Archangel's first, then quickly get yourself a Rod of Ages with that Catalyst. Once you have these, Skarner will snowball on his own, as well as Heal every time he levels, so that you can stay in-lane to perhaps fully purchase a Stinger or Nashor's Tooth the next time you have to go back to shop. This provides the Attack Speed necessary for Skarner to have most of his abilities off cooldown whenever he needs them. For his late game, Lich Bane makes his attacks between skills terrifying, and Rabbadon's Deathcap rounds out the build, pushing his AP high enough that Impale will do over 500 damage initially, and another 500 upon releasing the champ, allowing Skarner to kill squishies like Caitlyn or Vayne almost with a single spell, not to mention the insane distance you can cover using this build.
For AP Skarner's Skills, you really focus on Fracture for the massive healing it gives and Crystalline Exoskeleton to give you extra movement speed, attack speed to recharge abilities, and the Huge HP boost that AP Skarner is capable of. You put one point into Crystal Slash, however, because you can Fracture then Crystal Slash to consume almost all the healing marks that Fracture lays down. I've healed myself for 400 hp before using this combo on AP Skarner. Also, as soon as its available, you want to level Impale to give you the damage and utility that AP Skarner needs to be a valuable asset to the team.
I've chosen Ghost and Exhaust. Exhaust is helpful when chasing a target, in conjunction with Crystal Slash for slows, and Ghost really buffs Impale. You could also go with many other spells than Exhaust (Ignite for extra damage or Clarity for early game Mana for example) but by building Skarner pure AP and focusing on Impale, you don't want to get rid of Ghost simply due to that spell's usefulness with Impale. Flash-Ghost may also be viable, as it gives Skarner the ability to close/escape with flash, but then you're really selling yourself short on CC abilities, sustainability with Heal or Clarity, and the damage of Ignite, besides which, Ghost is still useful as a closer/escape in and of itself, especially with Skarner's speed already being as high as this build makes it.
Pros / Cons
High Survivability, Highly Sustainable Laning, Powerful Ultimate, Ultr-High Healing, High Burst Damage, Fast Repositioning/Lane Changes
Low Sustainable DPS, Low Armor, Low Magic Resistance, Highly Susceptible to CC, Expensive Item Build
Ultimately, building AP Skarner is all about focusing on only two aspects of Skarner, and that is his heals with Fracture and the utility/damage of Impale. This build cannot jungle, and winds up being a little light on sustainable dps, although Fracture and Empowered Crystal Slash will hit pretty hard, the focus here is on Impale. Using this build, you can Self-Heal tank similarly to Vlad and pick off high-dps, low hp targets (such as Vayne/almost any AP Carry) like an assassin. If the enemy team is light on stuns/pop-ups, you can even be confident in using Impale as an initiator after boosting your movement speed with Ghost and Crystalline Exoskeleton. You still need a team with a good tank (Alistair, Ammumu, Cho-Gath) and some sustainable dps (Vayne, Caitlyn, Garren) to make this work, though.