Not Updated For Current Season
If you want 10+ kills in a match, read another guide.
Now that that's settled, welcome to my AP/Support Hybrid Janna build. This build relies on the skilled use of Janna's ult and basic abilities to conquer team fights and push lanes hard in the mid-late stages of the game. Not to mention, you will be a farming machine.
Janna's passive gives her and her allies 3% increased movement speed. This included with the 3% from masteries and 8% base from L1 Zephyr, with movement through units included. Therefore, starting with boots at L1 isn't worth your time, especially with the 15% magic pen from the mastery and the base 8.5 from runes. Therefore, you should start by rushing Rod of Ages by getting the Sapphire Crystal. The extra mana will keep you laning longer before having to pop your mana pot. After that, Clarity is always available too. Once you get 925 gold, jump back and get the Catalyst the Protector. This will keep you laning virtually forever. If you're having trouble last hitting minions, pop back to base when you have 860 gold for the Blasting Wand for the extra AP to help your tornado and your slow. Once you finish Rod of Ages, you'll be getting close to mid game, so you want to get Sorc Boots for the extra Magic Pen.
The next part really depends on team composition. If you have an AP heavy team, grab Will of the Ancients first. The AP for yourself, and Spell Vamp and AP for allies is invaluable in team fights. 30 AP makes your AD/AS Twitch do an additional 30 damage per stack of poison with his Expunge. That's a possible additional 180 damage. Not too bad if I say so myself. If you're more AD and Tank, getting Soul Shroud in place of Will of the Ancients is not a bad call. Increased Mana Regen and reduced CDR can never go wrong. I still prefer Will of the Ancients, because it gives you 70 AP and 20% Spell Vamp for 2.1k gold, but Soul Shroud is an option.
Zhonya's Ring is self explanatory. 120 AP, plus 25% of your max AP into your AP, + the invulnerability active makes it the go-to item for AP characters.
Rylai's is such a good item late game, and I'll explain why. It allows you to use your tornado as a slow in place of your W. This lets you hold onto your passive movement speed boost, and makes picking off squishys more manageable. Plus, 80 AP and 500 HP never hurts :)
The Reverie is an interesting item. It gives you Health and Mana regen in the same item, which is awesome, but its the active that shines. If you ever have to build this item, it makes escaping and chasing so much easier as a team. Since you have so many ways to slow down the opposing team, an option to speed up yours makes things interesting as well. This is an optional item, and is personal preference ONLY. You can put whatever you want here. Guardian Angel increases survivability and lets you be a bit more aggressive, but you probably won't need it. Archangel's Staff is a good purchase if you feel you need to do just a bit more damage or need just a little more mana
You want to lane with someone that will take aggression off of you if you can't lane mid, or at least have the ability to pick off some weakened champions. Janna's Q, Howling Gale, is an awesome farming tool, but it's also one of the better harassing moves in the game. Use it early game with the heightened mana from the crystal to get minion kills and farm gold quick. When you put points into your W, understand that it is for the heightened movement speed, not for spamming. If you use the ability, it should be either to A.) Slow your opponent so your laning partner can take them out or B.) Getting a Champion kill. Save your mana for your tornado, and aim in the middle of the minions every time you shoot to make sure you hit every minion. Should champs get in the way, that's an added bonus.
You should have gotten Rod of Ages by now, and maybe even Sorc Boots. If their team is feeding hard, don't be afraid to drop the 1235 gold into Mejai's Soulstealer over Sorc Boots. Save your ult for emergency situations, such as healing your allies in a losing team fight, or pushing two enemy champions towards a turret in a gank. Don't forget to farm those minions. Help where needed, and try to rack up Kills/Assists as much as you can. With such high movement speed, ganking is a breeze.
Mid-Late to Late Game
Once you hit 13, you'll be putting 1 point into Janna's Eye of the Storm. This shield absorbs damage and increases attack power. It can be used on turrets as well, making you a great lane defender with your tornado and shield in late game. Once you build into Will of the Ancients, you should be trying to find a way to get a team fight going. Use your tornado as an initiating tool, and use your ult I.C.E. Zephyr is a good support attack, but try not to steal kills as best as possible. Since you can farm minions so well, letting the other champs have the kills is not that big of a deal to you.
Use your Eye of the Storm shield to not only defend squishies, including yourself, and also to help increase their damage to push a lane faster and more effectively.
Janna takes a lot of practice and patience to master, but she really is one of the most powerful support characters in the game. Stick with her, and I hope this helps in anyway. If you have anything you'd like me to explain better or add, feel free to comment with constructive criticism. Thanks for taking the time to read :)