This is a basic quick guide to Heimy. If it gets some attention then I will expand on it.

Heimerdinger is one of the best pushers in the game. Period. So good in fact that it is very possible to push a 2v1 back to their turret all by your lonesome. Not only that but the fun you will have playing as this little guy is amazing. He can push, kite, lure, harass, burst, and just in general faceroll overzealous champs. Let's skip all this foreplay and begin shall we?

This is completely personal taste.
You need to look for any combination of these things in your rune build though:

-Flat Mana Regen (Per Level is a waste because you only need the extra regen at the beginning of the game)
-AP
-Magic Pen
-Mana

These all go extremely well with this build.

Any form of 9/0/21 is pretty much the best way to go on Heimy.

Get you tear first. This will build into your Archangel's after you get your Sorc Shoes. So obviously the item's go:
Meki->Tear->Sorc Shoes->Archangel's
This is the beginning of the end for your enemies.
Rylai's is next because it allows for AWESOME kiteing around your turrets.
That completes the MUST HAVE ITEMS for any Heimy build (IMO)
The rest of the items you get are completely up to you.

I'm a big fan of Void Staff. The magic pen is amazing and the AP isn't too shabby either.
I'm also a big fan of Rabadon's. The insane AP shoots your damage through the roof.
Banshee's is a good item to help in kiteing.
Rod of Ages isn't bad.
Abysal is pretty good on Heimy as well.

Like I said, after Archangel's, Rylai's, and Sorc Shoes, the rest of the items are just play style and personal preference.

ALWAYS START WITH ONE POINT IN YOUR TURRETS!!! I cannot stress this enough. I see sooo many noob Heimy's grab their rockets first and it drives me CRAZY!!! So now that we have established that let's move on. One point in turrets, then work on maxing out those rockets first thing. Your rockets are your biggest damage output after your turrets and are AMAZING for harassment.

Early game: Turret, Rocket, Rocket. Always start this way. The rest depends on how the enemy is playing. If they are little cowards then completely ignore your grenade until you need it. If they are melee and are trying to farm your turrets then grab 1 point in your grenade so you can stun them as they run up to your turret and get some really good damage on them while keeping 12 gold out of their hands.

Mid Game: You will be grabbing your ult at every possible moment it presents itself because that CDR is very useful for harassment and keeping your enemies from farming your turrets. MAX YOUR ROCKETS ASAP THOUGH. I cannot stress how amazing your rockets are if you use them correctly. Next max your turrets.

Late Game: Finish off your ulti and grenade.

Turret placement:

Try to keep your turrets as close together as possible unless the enemy champs have AOE damage. This will allow for maximum damage output.

-While in any lane
Your turret placement will make or break you as Heimy. In mid I like to place my turret just slightly back from the middle of the lane and slightly towards top. Make sure it does not get in your minions way. This will allow it to shoot most of the minions and not be in danger of enemy minions. A similar position is good in bot and top lanes just putting the turret slightly towards whatever side the river is on. DO NOT PUT TURRETS IN A BUSH EARLY GAME UNLESS YOU ARE RUSHED. They will constantly give your possision away and will be, for the most part, under utilized.

-In bushes (for traps)
Always put them as far back as you can from where the enemy will be entering from so they will not prematurely give away the trap.

Rockets: Use your rockets only for harassment. Do not use them on minions until later in the game. This will allow for mana conservation early game and increased harassment. Wait for champs to be one of the targets (one of the 3 closest enemy units to Heim) and blast them. The damage will send them running and QQing all the way back to their turret.

Turret farming: Stop this from happening at all costs. This is why mana conservation with your rockets is so important. Always keep you turrets out of harms way from enemy minions. This increases their shakey survivability. Their range is pretty short so keep them kind of back against champs like Cait and Ashe who can auto-attack them without consequence. The second your turret is low from champion auto-attacks throw a new one down a little further back so as to avoid turret farming. 12 gold a turret can add up faster than you think.

Lastly:
How to destroy champions with your awesomeness. Have your turrets set up and be slightly infront of them. Once the champ comes at you throw your rockets out and run behind your turrets. As soon as they get to your turrets, pop your ulti and throw a grenade right at the enemy champ. The slow from your ulti should allow for easy stuns. Then use flash or ghost to kite them while your turrets RIP their health apart. Don't forget to rocket and stun grenade them at every possible oppurtunity.


***SPECIAL***
If you are facing another Heim I would actually recommend maxing your turrets first. It allows you to push faster at level 5 unless he is doing the same.

I personally always take flash and ghost. This allows me to almost always be able to kite like a pro and get away from ganks since Heimy is extremely squishy and very slow moving.

Good alternatives:
Clense and Exhaust would be good for survivabilty and kiteing.
Clarity if you spam your skills a lot.

Decent alternatives:
Ignite maybe to ensure kills on escaping enemies.
Heal if you are a little pansy. (I despise heal)

Bad alternatives:
Every spell not listed above...