Janna is an extremely versatile champion. Along with her incredible pushing potential she is also capable of escaping situations other supports are too slow to avoid. With this build you should die little, as it focuses on survival, mana, cooldown reduction, and a decent amount of AP to top it off.

Howling Gale
Janna's "Q" spell is Howling Gale. This is your disable, pushing spell, the reason why early game, you get left alone by anyone smart, and also why you're a great harasser. Most champions start out with 30 magic resist. If you build your mark runes with magic pen (only thing useful for Janna in that to be honest) your spells get past A LOT of their resistance. In fact if the thing above is correct, by level 18 she gets through 28 of their resistance. Unless the enemy has more in their items/masteries they have little resistance you your tornados. Early game this spell can easily win you and your team mate first blood.

Zephyr
Your slow spell should be used to slow an enemy in a one v one chase. Also can be used for last hitting creeps if your lane partner is a greedy idiot.

Eye of the Storm
Your shield should be applied to the damage per second carry(Ashe, miss fortune etc) or whoever is the lowest health/the turrent you are defending.

Monsoon
Use your Ultimate to push enemys away from their allies aswell as healing dying allies. Especially the carry.

Marks:
Greater Mark of Magic Penetration
In many others and my own opinion, Magic pen, and armour pen are the only decent marks. These marks give you the edge on your opponants early game and are also useful late game.

Seals:
Greater Seal of Armor
Janna starts out with approx 12 armour. Laning against two AD champions? Without these, you're first blood, and also a very easy target. As these runes are benificial both late and early game they're honestly a fantastic choice for Janna. Saves her practicly naked butt many times.

Glyphs:
Greater Glyph of Scaling Ability Power
AP per level. These keep your tornados hurting, improve your shield, slow, ultimate, whats not to love. You could get magic resistance/mana regen if you wanted, but personally i choose these.

Quintessences:
Greater Quintessence of Ability Power
Flat AP. This gives you close to 15 extra ap early game, which can easily save yours/your lane pals life. If you don't like these get something that makes you survive better/etc. Im just posting my personal preferance.

Sight ward:
As a support, you should keep lanes warded to help prevent ganks as well as your clavoyance you can protect your team with wards placed in useful locations. I'll put an excellent warding guide in the comments made by an excellent player. All support and junglers should read this guide as so many players don't use their wards properly. Janna has no problems farming with her tornado so therefore can afford to buy wards.

Mana Manipulator:
Get it if you're laning with a mana hungry partner like Pantheon. If you however are laning with a champion who uses energy/has clarity get the sapphire crystal as it later becomes part of your Rod of ages.

Sapphire Crystal:
Allows for more spamming, gives you a good mana pool to start off with. The health potions keep you in lane soaking up exp for longer.

If you want to get a Doran's Ring, go ahead, its a decent starting item. I just prefer these. Dorans I use on most of my solo laning spell casters but as a support you arent going to farm as much as the carries so keeping items you can use to benifit both yourself and team mate/for your later build helps.

Boots
Every spell caster needs her shoes, Janna is no exeption. Her passive and Zephyr bonus speed isnt enough, it makes her a good deal faster but doesnt replace a good ole pair of boots.
Unless the opponant team has alot of stuns, snares etc in which case get Mercury's Treads, i get Ionian Boots of Lucidity for the reduced cooldowns. If the enemy team has an Xin or Trynd intent on smashing you to bits get Ninja Tabi boots instead.

Rod of Ages:
Your core item. Provides a good hitpoint and mana pool aswell as a decent chunk of ability power. we want to rush this in so you're not as good a target.

Rylai's Crystal Scepter:
Personally i love these on janna. It turns her howling gale into a massive slow, allowing you to escape from almost anything. It also improves the power of your slow and adds in a chunk of hit points and ability power. These are optional, if you dont get these i would recommend you get a second rod of ages though.

Tear of the Goddess:
By now you have a decent mana pool, why not expand it. Get these and later turn them into an arch angels staff.

Frozen Heart:
Remember you're a support. Therefore you are there to help most of the time. While shielding your DPS carry, why not slow the opponants attack speed as well. You are the perfect choice for this item and it allows the tank to get more beneficial items for him/herself. Also provides a good amount of mana and armour, the cool down reduction just puts the icing on the cake.

Archangel's Staff:
All these mana items, what to do with them? Turn them into AP of course! I havent been simply getting you to stack mana for no reason. With a mana pool like yours you can pretty much spam as many spells as you like. Often a game will end before you get this item.

Abyssal Mask
Finally another aura based item. Provides a good aura for the teams ap casters, good for those games that last forever, good chunk of magic resist to protect you from those irritating casters, most of the time a game wont last this long though. Provides a bit of AP aswell.

If you don't feel like getting the Abyssal Mask go with a trusty Rabadon's Deathcap instead for that AP boost. Or a Zhonya's Hourglass for the great active and extra armour + AP.

If you and your team mate are simply dominating, get a mejai's soul stealer, if you die alot/are starting out with Janna skip that though. You dont want to be targeted simply because of your stacks, id recommend mejais for pro Janna's only.

Clairvoyance:
You need map awareness, as a support thats expected of you.
Clarity:
Keeps your mana up at the start, good for giving carrys mana to harrass better late game and during team fights.

Good to use on Janna
Teleport
Useful for ganking, good for getting around the map.

Flash
Great for jungle juking (escaping through the jungle) but i think Jannas speed allows her to get away with not using this.

Fortify
Better suited to a tank, but Janna is a suitable carrier of it if no one else has it.

Heal
I never use this spell but hey, that's not going to stop you. Heal is reasonable on Janna as she has no other healing spell until her ultimate. Up to you really.

Bad to use on Janna
Smite
Janna isn't a jungler. Nor should she EVER be used as one. Her Howling Gale is a dead giveaway.

Rally
Does anyone actually use this?

Ghost
What do you think Zephyr does? Exactly this.

Cleanse
Chances are you're dead anyway if you get stunned.

Revive
You are a support. Reviving to go kill that enemy that escaped on 40 health isn't your job, its better suited to ... anyone else.

Other offensive spells like Exhaust and Ignite aren't particually useful as you aren't going to be doing most of the killing. You will be keeping your team alive, yes. Harassing, yes. Getting 40 kills, no, unless your opponents are incredibly stupid.

Help section:
This build i think is balanced enough to prevent Janna from being an easy target, if this isnt the case please let me know :).
If you keep dying, get an extra Rod of ages. It really does keep you alive, even if you have to skip the rylais to do it.

Lane with a melee preferbly as you can harass enough to allow them good farm.
Pantheons love laning with Janna, if you can lane with one of them, perfect :). They will help keep you alive if they're a good Pantheon and you should use your Clarity and Mana Manipulator to help with their early game mana problems.
Poppy also loves laning with Janna. Allowing her to last hit half your creeps can benifit her greatly, plus you can give her easyer chasing with your shield and slow.
An ***asian would love laning with you as you are an excellent pusher, can shield them from damage, and can slow opponants to give easyer kills.

Janna probably never should lane with another support, exceptions are Morgana, shes alright with Sona, Teemo and Lux. Although these champions are better put elsewhere (mid generally as they can be used to carry), they can work with Janna.
Less offensive supports will be too squishy and you will likely die more often.

Id like to know how to improve this build, yes i will fix spelling errors etc. If you'd like to see something in this build please let me know and I'll add it.

I haven't included babysitting because Janna should share exp and gold with her team mate. She needs it just as much plus benefits her team mate more by not dying due to lack of items.