Janna has amazing mobility to begin with, but once she gets some items, it is so easy to stay relevant in fights while never dying. This build centers around her mobility as it's key to success with items like Raptor Cloak being a very strong early game spike in power for her. Let's break down how we use this build effectively.

How to begin?

Medallion > Boots > Wards > Cloth Armor > Boots 2 > Raptor > Majai's
Pick either Core 1 or Core 2 build based on what champions you're against. Core 1 is the optimal build, but Core 2 has some support necessaries that you cannot overlook sometimes. Depending on the game, you may only need the tenacity from Core 2 or you may only require the vision section.
A few champions that will force you into Core 2 vision: Vayne, Rengar, Twitch, Akali, Fiddlesticks, Kha'zix, Nunu (jung), Master Yi, Shaco, Teemo and Talon.
A few champions that will force you into Core 2 tenacity: Leona, Amumu, Kennen, and Veigar. Count the amount of stuns on the enemy team, if they have 3+, get tenacity please.

Mid Game

Janna's mid game is a roam game. Do everything you can to prolong your mid tower because the map presence it gives is huge. Focus on your warding and skirmishing. If you get low on mana, just go back. You can get back to lane super quick so it often isn't a problem.
Make sure to pick up Alacrity and Righteous Glory in both builds. RG gives you the mana and health to stay around, the speed to chase or reposition (for ult) and is generally a great item.
If you have faith in your ADC after seeing them in lane, and they are playing an ADC that scales well with on hit +attack speed (like Vayne, Kalista, Ashe, Yi, Caitlyn ect) then you can skip Mejai's and go for the Core 3 build. You will have less survivability with this build because you will be constantly shielding your ADC, just be aware of that and play accordingly. I would NOT take this build without a tank on team.

Late Game

Make sure you pick up 1 defencive item. Banshees is best in most cases but the others can be useful. Just make sure you have a reason you are buying what you are and you should be gravey.
Peel. Shield. Ward. Baron. Stay alive. Win game.
Zoning a key person from a fight can sometimes be entirely worth your ult. Zoning a jungler from a baron smite is a huge team win for example.
Catch out anyone out of position. If you have your team, that can even be a tank (just don't blow your ult to catch a tank). You should have Righteous Glory by now you can survive a full combo from most champions so it's not too scary to shield up, RG in and throw some wind around.
Careful of late game carries like Vayne and Tris, they have the ability to stick to you even with all your skills and movespeed.
Zzrot isn't as bad as it sounds but it is still likely a last item upgrade. It's good to distract a lane right before a Baron. Before, not during.

Raptor Cloak

Get it, don't bother upgrading it. As Janna, you are less likely than other supports to roam through jungle and go looking for those fights. Raptor Cloaks passive is almost ALWAYS on for you, combine that with the fact the the speed it gives is far superior to any item other than Boots of Swiftness and you're laughing. Literally. Spam /l
I'll let you in on another secret, because this item allows you to outplay anyone who thinks your are worth chasing;

This is one of the most fun items in the game.

9x Scaling Magic Resist Blues
9x Armor Reds
2x Armor Yellows / 7x Scaling Health Yellows
3x Gold Quints

This is my preferred build. Survivability is key to Janna, and resistances give you the damage mitigation you need when combined with a shield. Because you have a shield and max it first, I don't think health is necessary for flat yellows, scaling should work out just fine and reaches the same amount by level 7 anyway.

Often people don't like to run Gold Quints on a support which is fine, so if that is you, here's an alternate option.
9x Sacling Magic Resist Blues
9x Magic Pen Reds
9x Scaling Health Yellows
3x Armor Quints

Another option that is viable is the movement Quints, but I just don't know if they are necessary for Janna to stay relevant. Stacking too many stats into one area isn't always the best option.
3x Movement Quints

Janna is not a harass support. She excels at turning all in fights into her favor with CC, damage mitigation and then follow up chase. She is weak to poke champions that have good follow up on their poke like Morgana and Nidalee.
-Try to focus all your efforts on keeping vision up and shielding your ADC to mitigate damage in trades.
-DO NOT harass with your Q! This tip is for laning only. Come teamfight time, feel free to use it as a team siege weapon. If I ever see a Janna do that and it misses, I go ham on her and she loses that trade. Even if she lands it, it's nowhere near as good as a Blitz hook or a Morg bind.
-Rely on your ADC to harass. Your job is to shield their harass to make a favorable trade. You can shield yourself so that you can walk up to W poke, but it is just not as effective.
-AA to help your ADC cs where it is needed. Even out waves so less huge ones hit towers, rush that level 2 by hitting back minion on the first wave and front minions on the second.
-Learn how to last hit as Janna. Damn she hits hard! Often you find yourself in an open lane because you don't die as much as everyone else so you need to know this.

Janna is an amazing champion who adds a lot of diversity to the game. She has the strongest disengage of all champions, and is difficult to counter. She is a cheap costing, easy to use support seen in all levels of play.

Core 1:
Greater Stealth Trinket is the aim here. Mejai's is expensive and optimising a Sightstone before could make it obsolete. Just buy wards. I think everyone forgot that supports have the ability to do that, it's either SS or you're a troll. Not true.
-Buy AT LEAST 3 green wards and 1 pink before you get level 9.
-At level 9, always upgrade trinket. Do not wait, no item is more important.
-Keep buying Pinks all through the game. Don't be shy.

Core 2:
You need an Oracle's Lens so you will need a Sightstone. Priortise this over Raptor Cloak because you will get some defencive starts with it. Do not get a Mejai's. You won't have the money or the item space to keep buying Pinks.
-Get Boots of Speed then Sightstone.
-If you buy but you didn't buy the Sightstone yet. Buy 1 green ward.
-Don't get a pink until you complete a Sightstone.
-Upgrade Oracle's Lens when teamfights begin to get scary, usually around the level 11 threshold (of the enemy stealth champion, not you the support).
-Keep buying Pinks. Already established that there's a stealth champion.
-You will find yourself warding jungle more. Good.
-You will be seeking Jungle fights a bit more. If it looks like most fights will be over drag/baron, Raptor Cloak may not be the best itemisation.
-You will be tankier. Feel free to make a couple of risky plays. Especially if they don't yet expect Oracle's Lens.