Not Updated For Current Season
A costly build so you might want to be able to score a lot of cash or at least to solo your lane.
Start with Eye of the Storm, you do more damage on normal attack and you are protected against attacks, so you may be able to defend yourself against ganker at the start of the game (this ability saved me many times).
You go with Zephyr on level 2 and you can start attacking back on enemy players and with Howling Gale on level 3 you can start annoying them.
My items builds center around Nashor's Tooth, 50% attack speed is really great mostly against creeps and is good against players. Ability Power is a must with Janna so 55 is good. 10 mana regen per 5 second is great because Janna has low mana and her ability are really mana consuming and one of the most important thing in this item for me: 25% cooldown reduction. That's crazy. With this, the cooldown of Eye of the Storm is shorter than his duration, a spell you must always have on you.
After I got this item, I usually go for speed. Mercury's Thread is great for it gives a decent magic resist, a good speed, and reduces stuns and the likes by 40%.
Depending on my situation after that, I go with either Armor/Health or Ability Power. I usually use Doran's Ring at the start of the game to give a little boost.
I use Soul Shroud to reduce the squishyness of Janna with more Health and it also gives off a nice mana regen.
Fiendish Codex is one of my favorite, not too expensive and , again, ability power and mana regen!
Ignite for the DPS Janna might be missing to down bigger foe, and Teleport to get there quickly.
Masteries goes to the reduction of cooldown and the mana regeneration, but goes on the offensive a little to give Janna an extra boost.
Same thing for rune but I'll let you decide what to choose.
I think the priority for Janna should be made on cooldown reduction so she can attack more often and ability power come right after that to gives a good boost to those attacks.
First build of my favorite character, hope it's not too bad.