I don't have much to say in this section really. I've been playing league for several years, and blitz was one of my first champs so I decided to make a guide on him. This guide is unfinished, but I will be editing it and adding new material over time (all the added info will be recorded in the editing catalogue).

8/30/17-Blitz Supp Build origanal publish + Intro, Edit Catalogue, Pros/Cons, and Runes & Masteries created.
8/31/17-Leona, Vel Koz, Blitcrank, and Shen added to Blitz Supp Build's "vs Champs" + Combos chapter added.

Pros:
+Strong hooks that almost guarantee a kill each time you land them.
+Lots of damage for a support.
+Good follow up to hook.
+Has good playmaking potential.

Cons:
-Takes a lot of mana early game.
-Useless if you can't land hooks.
-Fairly easy to counter.
-Can be outplayed.

His runes are fairly simple. Movement speed quints to help him roam, AD marks for better poke/all in early game, flat armor seals for more tankiness, and mana glyphs so you can stay in lane longer early game. If you want, you can switch out movement quints with flat armor quints.

Blitz's masteries are pretty straight forward, but i would like to discuss them a bit anyway.

Cunning Tree

Wanderer vs Savagery - This one is obvious, you're not going to be csing without your FoTM (which makes it super easy) but you will be roaming.
Runic Affinity vs Secret Stash vs Assassin - You're not a jungler, and are going to almost always be with a teamate, so definetly go Secret Stash for the sustain in lane.
Merciless vs Meditation - Another obvious choice due to the fact you need mana way more than you need damage, especially in the early game.
Greenfather's Gift vs Bandit vs Dangerous Game - Greenfather's Gift can be knocked out immediately because we do not need the damage it provides. Between Bandit and Dangerous Game , I would lean toward Bandit due to the fact you will only cs with FoTM and need another gold source to get your items quicker.

Resolve Tree

Recovery vs Unyielding - This one is a little less indisputable than the previous masteries we have mentioned, but I still think that Unyielding is the way to go because Blitzcrank is a tank and although Recovery can be nice, the defensive stats from Unyielding tops it.
Explorer vs Tough Skin vs Siegemaster - Another slightly tough choice, but the
help Explorer gives to roaming trumps what Tough Skin and Siegemaster have to offer.
Runic Armor vs Veteran's Scars - This is pretty obvious. Only your passive benefits from Runic Armor , while Veteran's Scars boosts your overall tankiness.
Insight vs Perseverance vs Fearless - This is a hard choice. We don't really need Perseverance because it falls off in the late game where the regen is hardly noticeable. Between Insight and Fearless , it really depends on the enemy. If it seems like a hard match where exhaust is required to peel for your carry,
take Insight , otherwise, take Fearless for the extra tankiness.
swiftness vs legendary guardian - Another hard choice. I tend to lean toward Legendary Guardian for more tankiness, but Swiftness is a viable option too.
Grasp of the Undying vs Courage of the Colossus vs Stoneborn Pact - A fair competition between Stoneborn Pact and Courage of the Colossus , but I prefer Courage of the Colossus as it's shield is super useful, even after being nerfed.

Blitz has two main combos, QE(R), and WEQ. The first one is fairly simple, when you land a hook, follow up with an E for the knock-up then an ult (if you have it) for the extra damage and a little bonus silence so they can't flash away. The second one is actually not used as much as it should be. First, use your W to catch up to the enemy, then E them up, and when they try to get away, hook them back. These are a couple neat tricks that usually land a kill.*

Note: *It would be best if your team follows up to secure a kill.