AP Janna can actually be quite viable, and she is a strong solo mid for these reasons:
- Hard to gank because of her Howling Gale combined with No Unit Collision passive
- Extremely good farmer mid-late game with Howling Gale (If played correctly you should be one hitting caster creeps pretty early in the game)
- Good sustain when you use her shield effectively with her great poke, and build her with some health.

When playing Janna you should put down a Howling Gale and let it get fully charged, earlier on, you will have to auto attack the creeps to finish them off, but she is still one of the strongest and fastest farmers. Later on, when you get level 4 or 5 Howling Gale, farming will be ridiculously easy, and you shouldn't miss too many last hits, if any. Take advantage of your farm capabilities and get as much CS as you can, because Janna isn't a very strong damage champion if she doesn't get a lot of AP and Cooldown Reduction early on.

Pros:
- A lot of fun to play!
- Great farmer
- Good lane sustain
- Hard to chase
- One of the best poke / harass abilities in the game
- Eye of the Storm scales with AP so you have survivability
- Very good when ganking because of Howling Gale and Zephyr
- Her Monsoon can completely change the way a team fight is going

Cons:
- Somewhat difficult to play well
- Squishy
- Inconsistent damage
- Not very much burst
- All of the skins suck :<

For summoner spells, the reason I go with Teleport is pretty obvious, she is solo mid and it's really important to get back to lane as fast as possible and not let your opponent out farm you.
I go with Flash as well, I shouldn't really have to explain this one, it's almost an essential spell for anyone because of how versatile it is, it can be used to dodge skill shots when you are low, juke people out when they try to gank, and it has many offensive uses as well, like chasing or initiating fights. Other viable summoner spells for AP Janna are ignite because of her low damage output, or Ghost which works well with her passives for chasing/running away.
I don't recommend Clarity, if you are having early game mana problems, buy boots instead of ring, and get mana pots.

I go with the typical Utility and offense masteries, usually used by mages for the XP gain and the mana/hp regen along with summoner spell cooldown reduction. You could also go with Offensive masteries but I don't recommend them because the damage gain is not worth losing the bonuses from Utility. For Runes I go with:
- Greater Mark of Scaling Ability Powerx9
- Greater Glyph of Cooldown Reductionx9
- Greater Seal of Healthx9
- Greater Quintessence of Scaling Ability Powerx3

AP per level because you want to max out your damage late game when you have level 5 Howling Gale and level 5 Zephyr. In addition to that, I use cooldown reduction blues for more farm/poke capability, and hp yellows for survivability, overall these runes work fine, but feel free to use whatever you want, because I have not done all the math and I'm fairly sure there are better rune combinations for AP Janna, but I use what I already own.

Doran's Ring is usually my first buy on Janna, because it gives great stats for the gold early game, but take note that if you're laning against someone with good harass or poke, you might want to grab Boots and Health Potions in case they start harassing early. Other than that just mainly stack AP and I go with Rod of Ages and Rylai's Crystal Scepter for the HP because of how squishy Janna is. Obviously you need to use your judgement; if they stack nothing but MR, get a Void Staff and maybe Sorcerer's Shoes, but for the most part just stick to the items shown and you should do okay. In order to get the Hourglass, you need to sell the Doran's Ring(if you bought it, that is).

Janna is one of the most helpful champions you could possibly have around when it comes time for a team fight. She has a great impact on the outcome of fights because of her amazing CC. Make sure your team lets you get blue, because with that cooldown reduction + mana regen you will be able to span your Howling Gale and your Zephyr while still keeping your Eye of the Storm up on low HP allies. Your Howling Gale takes some skill to use correctly so just make sure you get it in a good spot. Also note that in team fights, it's primary use will be CC and not damage, so don't hesitate at all to make it release before it's fully charged. The most useful way to use it in my opinions is whenever an the enemy team tries to dive on one of your carries or squishies, knock them up in the air and instead of your carry being in trouble, they will be fine and even get some free hits on the other team. Your Eye of the Storm is extremely useful for saving low hp teammates, like if you see a Karthus, or Caitlyn ult incoming, pop it on the lowest hp ally. It's also useful for saving people from tower hits. Your number 1 ability in team fights is your Monsoon. It has the potential to turn a team fight that would have resulted in your team getting aced, in to your team picking up an ace, use it when most of your allies are low, and enemy champs are within knockback range, even if you don't decide to stay and fight after the ult, it still saves you and allows you to retreat safely.

Thank-you for following my AP Janna guide for soloing mid.
Just remember when laning to farm as much as you possibly can, and don't try to dive them because you don't do tons of damage like other AP carries. For team fights, it's pretty self explanatory - just shield teammates that are low(YOU should be top priority for Eye of the Storm), and use your Howling Gale at the right time to help your team win the fight. Remember that your ult is amazing and can really change the outcome of a team fight if you are losing, so use it wisely! Most importantly, have fun with AP Janna!

Also: Remember to take advantage of her Zephyr passive, when running from ganks or enemy champions, try to stay in the middle of the lane and go through as many creeps as you can, because your opponent will collide with them and it will buy you more time to get away.