This is my way of building Heimerdinger, and I find him rather underplayed. He's very potential, but only if you can create your own battlefield and your team fights in it.

Magic Pen. Marks: These give you some good magic penetration, and is generally a good pick for marks on ap mid.
Mana Regen Seals: These are very vital for Heimer's early game, His skills use up a lot of mana, therefore having early mana regen doesn't hurt a bit.
Magic Res Glyphs: Heimerdinger is a very fragile champion early game, easily ganked and killed. But at least to possibly live through the enemy mid champions burst, magic resistance is a good choise. Also consider Health per level seals, if you're certain you won't get bursted down early game, and the lane is going to be all about farming.
Flat AP Quints: Having the +15 AP @ Lvl 1 is generally a good pick for mid champions.

21/0/9 masteries are pretty basic ones for ap carries, Taking the mana per level for maximum AP gain and not running Out of mana through archangels.
Taking the mana regen since you can't have enough of that early game.
Buff duration for blue buff.
You can either get the 0.5% movement speed increase or the Recall time reduction depending on which ever u wanna get.
The rest of the offensive tree is self-explaining.

Starting with boots + 3 hp pots is a pretty general way to start mid lane, but if you wanna harrass a bit more get 1 mana potion and 2 hp potions.
Early-game Chalice + Tear is prepping up for the farming and staying alive.
Sorcerer's shoes add quite some damage to your spells, also giving you the movement speed that might be required to get away or get to certain situations at this part of the game.
Then rushing Rod of Ages, to get full stacks on it. You get a bit tankier, you get more mana, and the mana from RoA is also added to the Archangel's staff passive later on in the game.
Why Rylai's next? You're still quite squishy, you need the sustain, and also your spells will slow the enemies hit from now on. This will deal a great impact in the team fights right about now.
Rush Rabadon's or Archangel's, which ever you prefer at the time. My personal recommendation is Rabadon's first.
Going for the Athene's unholy Grail as your last item. If you get this earlier than most people have their full builds, You won't run out of mana in team fights and will carry the game depending on your position.
After your full build, get The Blue Elixir for more AP & CDR, going for the red elixir for bonus health after that, getting oracles to spot invisible enemies or wards, and finishing up with the green elixir for attack speed & Crit chace - 'Cus hey, why not?

Getting your Turret's level to 3 while aiming to max out W-skill First is the key part. You get to put down 2 turrets dealing good damage, while bursting people down with your W. Maxing E-skill last because I believe it to be the least efficient skill for heimerdinger, but good to get early level on it in case of a auto-attack jungler gank.

Flash = Safe getaway, or flash + W for a last hit on a kill.
Ignite = Reduced healing, + true damage over time. Why not? You can also pick:
Heal if you believe you might get bursted down quickly, or you believe you can't sustain enough.

Heimerdinger is a very underplayed ap caster, mostly because it requires certain positioning in team fights and for team fights, which is very hard in solo Queue, Because teams don't always want to listen to the brainiac at mid.

I recommend counter-picking to be the most efficient way to win ranked games, but Heimerdinger is a great balance out for example: Anivia. When the lane is all about farming, and your team will listen to your late game plans, Heimer will work out wonders.

Pros: Great late game AoE's, ok chasing capability, Great sustaining bursts


Cons: Very weak early game, doesn't work well with none-communicating team, Most people play Heimer out of position.

In team fights you should always aim to for example trap baron, or put up a trap in the enemy jungle with ur team, waiting for someone to come greet your turrets for a cup of Tea, while U rocket the sh!t out of them!
Playing Heimer is all about the battle of Wits! If you can get your team to keep trapping the enemy team, forcing them to fight where you've placed up your turrets, The team fight should be won.

Passive: Heimerdinger heals nearby structures (Turrets, Inhibs, Nexus, His turrets) passively over time.
Q: Places down (Rank1, 1 turret, Rank 3-5: 2 turrets) Turrets shooting at enemies with rapid speed
W: Hextech minirockets, fire out to the 3 closest enemy units, dealing great damage.
E: Throws out a slowly moving stun/blinding grenade, if hitting dead on, applies stun effect.
R: Passive: Gives Heimerdinger Cooldown Reduction. Active: Buffs Q & E skill, healing all his turrets to full health, causing them to slow all enemies hit, and applying 5 instead of 3 Minirockets on shot.

Place your turrets between the middle of your lane and your tower, keeping them up and harrassing with your W skill to farm up all you can.