As my first build, I decided I would use the champion I love the most, Blitzcrank! I love Blitzcrank. His hooks, if used right, can be the deciding factor in a game. Getting your ADC fed with Blitz should be easy if you can pull good. I started playing Blitz around lvl 20 and I fell in love. He is THE most OP support in the game and one of the only supports that can somewhat carry a team. This is how I play and support with Blitz. Feel free to leave any comments on how I can improve!

Most of these items are purely situational with the exception of the Aegis, Aegis is a necessary for any support.
A good example of a situational item is the Soul Shroud. I rush a Mana Manipulator when laning with and Ezreal or Corki. The added Mana regen gives Ez and Corki more poke presence, and the extra CDR helps pretty much anyone!
Double GP 10 items can give you enough gold to be buying wards and still get an Aegis.
Important Item #1:
WARDS!!!
Vision is necessary to win. Ward constantly! Be smart too. Place a high ward on dragon if they have a jungle Nocturne or Rammus ect. otherwise you can get away with lower quicker wards with any common jungler. I.E Udyr, Lee Sin, Amumu.
Get Zekes if you are owning lane or have a ADC that uses life steal or works a BT right away, like common for Vayne. But I can NOT stress enough to WARD!

His hook first. It can be great for a first blood, invading, and for lane pressure. I then max his W. The movement speed is great for getting in position to pull someone and makes up for getting Merc Treds instead of Movement Speed boots (which I find useless.) Also, your E doesn't do anymore damage when you level that up, you only gain a cool down boost, making it useless to upgrade your E before your W.
RQWE

Flash and Exhaust. Exhaust is a must, flash could be replaced with ghost, but I wouldn't recommend it, you have a built in ghost already.

Getting runes for Mana, Magic Resist, and Armor will give you the slight tanky advantage you need to stay in lane and survive if you ever need your passive to save your life. You shouldn't need mana regen if you don't spam your hooks. Be smart when hooking and a Philo Stone should be all you need.

Be smart when you hook. DO NOT SPAM YOUR HOOKS. You will waste your mana rendering your passive useless and making it harder for your ADC in lane. If you go against another good bot lane, they will take advantage of you being OOM (Out of Mana.) Also, whenever you get a hook, ult. The silence helps a lot, and can really chunk whoever you are pulling to make it an easier kill for your carry.
Your combo is simple.
WQER, if you miss the hook, then don't E or R! Save mana and have a strong lane presence.

Blitz is THE greatest toller in the game.
http://www.youtube.com/watch?v=pAPYk_C2ZZU
That is a great example!
He is a **** ton of fun if you can get good with his grabs.
AP mid is also a bad, but really really fun idea.