Here I have created two different builds for Heimer. Team 1 is for Classic and Team 2 is for Dominion. I quite enjoy playing Heimer and if played correctly in the early game, he can be quite powerful late game.

This is my first full build and i am still working on it.

Play defensively with Heimer until you start to get more health with the Rod of Ages. You are far to weak and slow to be caught out by the other team.

Only use your skills on other champions unless you are safe (there is no way they can attack you) and try to have a Turret ready to go at any time. If chased run past your Turret and hit your ult, while still using your Hextech Micro-Rockets everytime they come up, and the CH-1 Concussion Grenade. Once the chasing champ is clear of your Turret, place another down to slow them further. You want to get your Turrets to just overlap their ranges to provide you the most support. If you are too far away from help or safety let a DPS close in on you and place your Turrets down, blind him, then rockets and then let your Turrets do the rest. Use your ult for the damage over time if it is going to get close.

Classic / Team 1:
Getting the Tear of Goddess as soon as possible will help later game giving you more mana (Unique Passive) and which in turn when it is upgraded to the Archangel gives you more Ability Power (Passive).

Next the boots are a must as you will find with Heimer, everything moves faster than him, including wards. Boots depend on the game and who you are up against but generally Sorcerer's Shoes are the way to go.

Rod of Ages is next in the build, either get the Blasting Ward first if you are dominating your opponent or get the Ruby Crystal if you are getting worked. It is pretty important to get the ROA early game to get the benefits of its Passive.

Next it really doesn't matter too much what order you get the items in, but if your are still getting worked get the Rylai's Crystal Scepter for the health, or if you are dominating get the Death Cap.

The last item, the Abyssal Scepter can be replace with any other item, it is more of a luxury item. If you find yourself in the middle of the team fights, maybe look towards a Zhonya's Hourglass.

With these items you will have increased your health whilst still improving your AP, increasing your chances of survival if caught out by the enemy team.

Dominion / Team 2:
Still to come.
Basic points are to get as much health but still get enough AP to be useful and push/hold your lane.

Maxing out your turrets is the biggest priority. It helps both with farming but also gives you good defence against the other champs if they push you. Whilst laning, use 1 of your turrets behind the line of minions, play defensively at the start and don't push too much until you get your boots or ult (as you are way too slow to avoid a gank/attack). The first turret wants be minion farming for you as much as possible, but pointless placing of the turret will 1) get it killed, 2) leave you with no mana and 3) be on cool down when you need it most. My placement of my second tower depends on the other team. If no jungler (and i can trust my team will call MIA's) then I place it in my lane so that if pushed i can fall back to the second one, either deterring the attack, killing them or if i have my ult, stopping them from catching me completely. If they have a jungler (or can't trust my team) then i will place it in the bush right on the edge of the river. It acts as a ward that will last until re-positioned (this is another reason not to push with turrets too much) or until destroyed. Very good spot to turn a gank away before it even happens. Never place your turrets in the two bushes on the edge of the map, as it draws minions in and then they attack you (or teammate), not your turrets.

Secondly max out your rockets so that you can harass the other champs as much as possible. This is a very vital skill and if used correctly will 100% of the time hit a enemy champ. As with most AP champs, you can burn through your mana very quickly, DO NOT waste this skill on minions unless you have Blue Buff, and even then, be careful getting caught with this on cooldown, its shear damage can turn away an attacker if not simply kill them with the aid of a turret.

I don't get the CH-1 Concussion Grenade until the very end, as my first two skills are my big damage ones. The grenade moves so slow and can easily be dodged by a medium-good player. It is however ever useful against DPS champs like Yi, Trynd or Warwick, and if placed correctly can blind any of them and then your rockets and turrets can do the rest.