If you want to be a Janna carry, this guide can help you achieve that goal. A small notice to players though: This is more for winning games rather than getting killing blows. You might go negative but if you play effectively, you will win for your team.

Howling Gale: (Active): By creating a localized change in pressure and temperature, Janna is able to create a small storm that grows in size with time. She can active the spell again to release the storm. On release this storm will fly towards the direction it was cast in, dealing damage and knocking away any enemies in its path. The distance traveled by the whirlwind increases for each second it channels.
Range: 1700
Cooldown: 10 seconds
Damage: 60 / 85 / 110 / 135 / 160 (+0.75 per ability power)

Info: This is your friend, you use it at all times. It has many different uses. Mainly, this is used to push creeps at a good range. With the range of 1700, you can safely stay out of range while pushing creeps. This is an amazing spell and it really makes people hate Janna.

Zephyr: (Passive): Janna summons an air elemental that passively increases her movement speed and enables her to pass through units.(Active): Janna launches her elemental to deal damage and slow an enemy's movement speed for 4 seconds.
Cooldown: 13 seconds
Range: 600
Damage: 60 / 115 / 170 / 225 / 280 (+0.8 per ability power)
Slow: 24 / 30 / 36 / 42 / 48 %

Info: This ability is okay; the main reason you don't go into this until late game is because Howling Gale and Eye of the Storm are much better. Towards late game, this will come in handy for slowing people and escaping situations by moving faster.
Eye of the Storm: (Active): Janna conjures a defensive gale that shields her target from incoming damage while increasing their physical damage for 10.5 seconds (can target Turrets).
Cooldown: 10.5 seconds
Range: 800
Damage Shielded: 80 / 120 / 160 / 200 / 240 (+0.9 per ability power)

Info: This ability is what keeps you in lanes and helps you maintain your own tower. You keep this up mainly when the enemy is trying to get that one spell off, or you have an annoying ranged attack damage champion that tries to harass you. The greatest benefit about the shield is most likely the fact that you can shield your tower. If you see the minions start pushing it, you put it on, HG [Howling Gale] the creeps and repeat if necessary.
Monsoon: (Active): Janna surrounds herself in a magical storm throwing enemies back. After the storm has settled, soothing winds heal nearby allies while the ability is active. Enemies that re-enter the storm have their movement speed slowed by 40%.
Cooldown: 120 seconds
Range: 725
Heal per second: 90 / 150 / 210 (+0.35 per ability power)

Info: This ability is great as a whole. Your team will thank you later on for keeping them in fights with this ability. If you solo middle, this will definitely keep you in your lane. In some situations, you might even run in front of a fleeing enemy, pop it off for less than a second, and have the enemy thrown into your teammates.

Teleport: This skill slot can be mixed around if necessary, depending on your teammates.
Clarity: Oh boy, this skill is a must have for Janna. Even with Chalice you are needing mana if you play your lane right. This will most likely save you, this will most likely be the difference between life and death. (for most situations)

Here are some others if you don't want teleport:

Fortify: This is my second choice if I don't want to teleport around the map. Oh, your tower is getting beat on while you are at base... BAM! Minions die and they run away, buying you more time. This is better for the Jannas that are newer to the tower pushing, and if you know how to play Janna, this is overkill.
Ghost: Well, it's just a great escaping spell, but you have your Howling Gale to help you with that.

The rest are mediocre so unless you are 100% sure its good for you, then go ahead.

Starting out:
Meki Pendant: This item is good for keeping your mana regen at a steady rate. If you want to stay in your lane, this item works out for you.
Tear of the Goddess: This item is great for keeping your mana up throughout the game. It's hard to not have this item when you spam your abilities. Overall it brings your mana up quickly mainly because you spam your abilities a lot.
Mercuries Treads: This item is good for stuns and ap characters. For most games, this works out. If not, you can use...Ninja Tabi: This is for the heavy melee such as tryndamere, twisted fate, etc. If you choose this item, I would put your defensive mastery into Nimbleness for the speed boost and added dodge.

Aegis of the Legion: By this time, you should be towards midgame, so this item goes towards making your teammates less flimsy.

Frozen Heart: This item will help you with cooldown, mana, enemy attack speed, and armor.

Soul Shroud: This item is good for finishing off your cooldown reduction and also giving you that added health.
Archangel's Staff: This item is great to add a little oomph to your damage output. The mana you have end game really goes with the 3% AP.

The last item I leave open because from there on its situational.

Guardian's Angel is good for pardoning that long death time.
Zhonya's Ring is good for some added oomph.
Banshees veil adds more survivability.
Any other that seems fit will work.

BG: Beginning Game
MG: Mid-game
LG: Late Game
HG: Howling Gale
EotS: Eye of the Storm
Z: Zephyr
MO: Monsoon

BG:
Level: 1-11

Most beginning games for people last until level 6 or 7. However, Janna, has a different way of playing the game. Her main focus in the game is push, push, push... and it has served me well. Janna, unlike most players, focuses on getting minions kills for money, rather than ganking around the map.
In the beginning game, you

NEED

to spam your HG. A common mistake that I've seen with Jannas is to target the enemy champions. If you do that, you just wasted mana. You always target the minions, and always get the whole wave of them. The main idea of the tornado, is to get the opposing minions to no health, and finish them off by another HG or by attacking them. This trick will always keep your minions pushing, and the enemy champions tower hugging. Even if they tower hug, you can still spam your HG, thats the great thing.
Probably the best game I've had during BG involved destroying their tower during the 4 minute mark. Our teammates were impressed. The main idea is that you keep yourself alive while throwing tornados at the minions. Keeping yourself alive as in shielding yourself and fleeing when necessary.
That brings me to my next main topic, EotS. This spell will help you, your teammates, and your tower. It will save you from so many different gank and escape attempts. I'm not telling you to spam it whenever it's up, I'm telling you to put it on when you feel threatened.
Some of you may think Janna is not a carry, or that she is just a support. Well that may partially true for some players, but my secret makes her the ultimate carry. What is the secret? Keep on pushing your lane. Who cares if your friends up top can't keep a lane, just stick to yours. When your opposing lane goes and focuses somewhere else, you destroy tower. When they come to kill you, you just use your HG, shield, repeat(If you have Monsoon, use it too)and escape.

MG:
Level: 12-18

This is when the support aspect comes up. After you successfully pushed your lane one or two towers, it is time to head over and help your friends. If your team is grouping up in one lane, it is best to keep on using your HG until a fight comes up. When you see enemy champions pop up, then you start targeting them with your HG. If any teammate gets targeted, shield them and possibly use EotS if they lose enough health. Your goal is to keep all friends alive while keeping HG on the enemies.

LG:
Level: 18

This is where Janna becomes a dedicated support. With her cooldown reduction and mana pool, you can keep spamming your abilities when necessary. LG is very much like MG, the only difference is the items you should have by now. There isn't really that much to say about LG.

UPDATE:

11/20/10: Fixed the Janna build to include Tear of the Goddess. I found this item to work mainly if you have mana regen/5 runes. I wouldn't get Archangels until late-game.
Also changed the mana regen/5 runes into mana regen/5 per level runes.
Added Archangel's Staff for end game to finish your Tear of the Goddess.

3/9/11: Changed guide by adding chapters.

Thanks for looking at this guide.

Hope you enjoy this guide and good luck with Janna!