PROS:

Great pusher
Fun to play
Nice farmer
Does much damage
Only few champs counter him
Good skins

CONS:

Squishy
Slow
CH-1 CONCUSSION GRENADE is the most difficult skill shot in the game
Hard to master
Your teammates will underestimate you
Very item depending champion
Mana hungry

Boots of Speed and 3 Health Potion are good starting items on Heimerdinger because he is naturaly slow and squishy

Heimer is very mana hungry at so u need Chalice of Harmony It has a great mana regen passive + a decent amonut of magic resist.

Now the problem is that u dont do much damage and u need ability power. Needlessly Large Rod is a perfect item to get a decent boost of AP.

As i said before, ur really squishy and u should build him like a little tank so go get some armor and buy Zhonya's Hourglass. It gives u much ability power, some serius armor and has a great passive.

Now its time to get a lil bit faster, so upgrade ur boots into Sorcerer's Shoes because there is a great possiblity that ur enemys will buy some magic resist, and penetration u got out of ur runes isnt enough anymore.

Ur enemys also buy item to defet u, and u are still an easy target so get more tanky by buying some magic resist. The best thing u can do is to upgrade ur Chalice of Harmony into Athene's Unholy Grail U'll now have a decent amount of ability power, enough mana regen and short CD.

Enemys will be afraid of u and they'll focus u. Time to get even more tanky. Buy Giant's Belt and when u have an oportunity upgrade it to Rylai's Crystal Scepter. Its a great item. More ability power, large amount of health and a really usefull passive, perfect for chasing people and very usefull for escaping.

And now something some of u will say that it had to be done long before. Rabadon's Deathcap
A must have if u play an AP champion. But I think is not a good item on Heimerdinger in the early game because he has no escape mec., he is too slow to run away from a gank. Read my strategy of playing him and u'll understand why I dont build this item in early game.

The final item u need is Liandry's Torment. I choose this because it gives magic penteration. U need this because by now almost all ur enemys should have some magic resist. It gives u some health and it has a great passive which gives u some damege over time. This is good because the enemy can hardly calculate the amount of damage u'll deal to him.

There are 3 other items I like to buy when I think Liandry's Torment wouldnt be usefull enough.
Void Staff buy it when ur enemy has a large amount of magic resist.
Will of the Ancients when ur enemy team dont have much magic resist and u need more sustain
Morellonomicon if u need even more CD and if u have to chase ur enemys to kill them.

H-28G Evolution Turret are your greatest source of damage. Place 2 of them one next to another but enough distant to not be destroyed by 1 AoE ability. They do large amount of damage, and lower enemys magic resist. At lv.5 they do AoE damage. Really easy to farm whit them.

If u want to kill, u have to be patient and wait the enemy mistake. Usually people underestimate those turrets. U have to keep in mind that ur the bait. When the enemy start attacking u, place your self in the middle of the 2 H-28G Evolution Turret u placed before, when he comes in range of the turrets use CH-1 CONCUSSION GRENADE so he get stunned, leave the turrets do damage, and when he starts to run away, use Hextech Micro-Rockets

When u get ganked, go near your 2 H-28G Evolution Turret and use your ulti UPGRADE!!!.
There's a great chance u'll die, thats why I like to buy Zhonya's Hourglass as soon as possible. After 2 sec, they'll be almost dead, stun them whit CH-1 CONCUSSION GRENADE and use Hextech Micro-Rockets. An easy double kill.