Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
Since Heimerdinger is very mana-hungry, I've found that mana regen runes would help him during early game, but also placing mana/level runes as well for late game. In addition, putting in Spell Penetration runes and HP/level quintessences are a plus.
I've done a 9/0/21 build for Heimerdinger, with the Teleport bonus because its pretty cool to teleport to his turrets and continue on with the match. I also did some points into the magic-portion of the Offensive tree, giving him an AP boost along with cool-down reduction (on both Offensive and Utility) and spell penetration.
Back before I had mana runes I had to rely on Clarity, but now since there's mana regen runes, you'll be regenerating mana so fast you'll have no need for Clarity. I would suggesting going for Teleport as your first and have the second be anything you want.
I'll have the second spell set as Clarity, but you don't have to get it.
In my opinion, the best item to start with is either the Mana Pendant or Doran's Ring. I believe it all depends on if your team wants to do a starting gank. If it's a yes, go for Doran's Ring. If not, get the Mana Pendent. If you start out with Doran's Ring, sell it when you head back to base for the first time and start working on Chalice of Harmony.
You can also swap Ryali's Crystal Scepter for Rod of Ages if you like. Gives Archangle Staff yet another boost when you get your extra mana.
Note: Zhonya's Ring is suppose to be Rabadan's Deathcap