Heimerdinger may not be the most sought after ap carry, but he can definitely hold his own with his spells. It's probably the fact that he has little control over his turrets and rockets, once he unleashes them on the world. The other problem maybe that he is incredibly slow. So those two things are what most likely make Heimer unpopular among the common lol players.

I personally run ghost and clarity because I need a get away spell, and no matter how hard I try or what mana regen I run, I end up oom (out of mana).

I rely heavily on heimer's turrets so I want to get to lvl 3 turrets so I can have 2 turrets quickly. I even occasionally will for go the concussion grenade to get a second turret early. The real big time dmg is done though with the rockets. So between your turrets and rockets you can really upgrade how you want to play heimer. Never skip a chance to upgrade his ulti, because it gives him cooldown passively, along with upgrading his rockets and grenade for a short time.

Heimer is practically if not the slowest champ in the game. So to save him from ganks I normally go back at 1100 gold and get those. Then, the other problem with Heimer is that he is squishy. So I get a catalyst next, and if things are going really well a rod of ages straight up. The rest of the items are up to you when and in what order you get them. I prefer rod of ages over rylias because it gives me mana which eventually builds into the archangel staff. The archangel staff attempts to fix the mana problem that I have every game. If you can't stand how slow heimer is get him a lichbane as soon as you can.
I did end up including zyonas because it can save heimer in a pinch. While his turrets or teammates do work for him.

Magic penetration and ap are my highest priorities for heimer. I've tried different mana regens and what not and it takes too much away. I would rather say "oom" and go back then not be able to deal the finishing blow. REMEMBER I'M RUNNING CLARITY

The 9 0 21 gives Heimer the most cooldown, speed, mana, exp, and SPELL VAMP. I usually mid with Heimer and I almost always hit 18 before everyone else hits 16. This gives more hp, stronger spells, less cooldown. The gold and health regen are enticing but I can't give up the spell vamp and cooldown. Heimer already has a bunch of health regen. I am making the assumption that this passive that heals towers, his turrets and allied champs also heals him so lvl 18 he has like 39-40 hp per 5.

Leaving mid when minions are pushed and putting your turret in on the wraiths and fire rockets. Late in the game I've had my one turret take out 2 spawns worth of minions at wraiths. Remember that turrets do not have an expiration time. They are either killed off or replaced by you wanting another turret in a different place.
Place turrets far enough away so they don't get hit by the same aoe spell.

Heimer is great at helping your team escape a fight, it happens to me a bunch when I'm late to the party ( fight) so i plant 2 turrets on the way of their escape path and pop my ulti.

Landing Heimer's grenade is probably the hardest thing to do. You sometimes think you land it perfectly and they walk away. The grenade is slow enough that you either use it to extend a stun, root, one on one fights where they don't move, or guess where they are going and land it. The good thing is that even if you don't hit it, if it lands close enough it still blinds, so pick ad carries or their big dmg dealers and hit them.

Heimer's rocket's hit the closest enemy, and it means closest. I've hit creeps in the jungle when I'm trying to finish off a champ, very frustrating. So pay attention to what is closest to you when you fire it. Also it is key to use your ulti first so you get to fire 5 rockets instead of just 3.

The other unique skill is deciding when its time to turn tail and run. Since Heimer is slow, if he doesn't leave before everyone else leaves, he is likely to be left behind and killed.

I like to push my lane with the turrets on purpose so I can go gank, help another lane, or just go get dragon. Teammates can teleport to your turrets, so if you hide one they can teleport in.
If the other team is about to kill one of heimer's turrets he can replace that turret by placing another one. But if he has 2 turrets it has to be the first one he placed, or u can quickly place 2.

Pros: Great lane pusher
Nice range with his rockets
Has a blind and maybe stun depending
Cooldown built into his ulti passive
Late game his turrets lower Magic Resist
Holds lanes very well with his turrets and other spells
Beefy Caster
HE HEALS TOWERS, HIS TURRETS, AND TEAMMATES!
Has an amazing taunt that you should use at the end of the game :)
Cons: Takes a while for Heimer to get some serious ap
He is a really slow champion.
He requires a solo lane, lots of cs, or fed some kills.
Chews through mana in no time
If his turrets are killed he gives the other team 12 gold.

Heimer throws a wrench.
His turrets have more MR then armor.
The turrets attack at 1.250 attack speed.