Janna is a great utility support. She doesnt have lane sustain (heals, other than her ultimate, like others do but you can constantly poke and the slow that you get from W allows your carries or jungle to catch up to the enemy easily. Maximizing W first gets you the most movement speed to fly around the map. Janna can essentially lock down an enemy by chain slowing them allowing anyone on your team to catch up to them. Janna is also a good champ to have if you want to escape engagements by knocking enemies up or slowing them which can break the engage often.

You want to make sure that you dont always throw tornado's (Q) in the same direction, make it seem like it is all random. I like to go into a bush quickly and toss one down and if you do it right you can push the oppoposite team into the tornado.
For an aggressive lane you can take Ignite to either ensure kills or melt the enemy faster to let your carry get fed fast and early. If you want to help secure kills without the threat of accidentally taking the kill then be sure to take exhaust as it will lock them down combined with W and allow for easy kills.

There really is no counter threat to Janna as long as you are constantly moving and use your W wisely. If you are using W early to poke that is great, but later in the game you will need to make sure that you have it up when needed to get away. If you use it and you lose your movement speed getting out of a sticky situation will be tricky. Boots of mobility are great to let you fly around the map and help as many lanes as possible but if you lose the passive and you dont have W, you are more than likely probably screwed.

Something to think about; dont always use your ultimate to save (heal) your teammates. You can use the ultimate offensively to either knock enemies into the turrets, back at your ADC or if you use it to pin someone to the wall it will secure the kill as well.

If you want to go more aggressive and build AP there are many options to choose from. Luden's is great and will boost your movement speed. Crown is another good one for "safety" if you feel you need it.

Late game Janna is very powerful once you get full build. You have shields that are extremely strong, a slow that is almost never ending, and a ultimate that can save your entire team if they are all around you. You should always try and position yourself in the back line as you are powerful but very squishy and will get blown up very fast. A good enemy team will try to focus you and take your utility out of the team fight.