Blitzcrank is a powerful melee ranged support.His abilities deal very high damage while he has the body of a tank and so such health his mana is his most imprtant spell that allows him to use his abilities BUT his passive is being increased by it!

To play as support u may either increase his survivability or increase his damage with his Q and his R!
To increase his damage u will glyphs for cooldown reduction per level marks for magic penetration seal for mana regeneration quintessenses for ability power per level.
To increase his defending skill u will need seals for mana regeneration per level marks for
magic resistance per level glyphs for armor and quintenssenses for cooldown reduction per level!

First mastery build is for ability supporting getting cooldown of CV reduced and its duration increase while getting getting some extra Cooldown reduction ability power and magic penetration.
Second is for more defending supporting while not decreasing the cooldowns of ghost and flash increasing movement speed by 35% so u can escape easier in the end increasing the armor and the magic resistance to max out his defending powers.

For me the build should be the same on blitzcrank but there r some items that u can get instead of the Build i use
These are:
Mercury's boots to get rid of cc effects used on you some times
Ionian boots of lucidity to decrease your cooldowns even more
Morelo's evil tome for its cooldown reduction its active effect and its GP5 item that can be built instead of philosopher's stone
Randuin's omen to give you more armor health and for sure cooldown reduction
2 items with cooldown reduction are enough
Archangel's staff instead of manamune to increase damage of Q and R instead of increasing his auto attacks

Remember your 1..2..3..4 combo
i make it 1..3..4 and then 2 remember not to last hit the enemies because you mustn't kill anything because your team they might call you a noob!
Late game you may use your ultimate to kill groups of minions cuz with all that cd reduction it will have like 18-20 seconds
You can use your W and your E to damage the turrets faster.

Ghost and CV are very important you can use your CV to prevent ganks whenever u think somebody is in the grass the cooldown is so low that u will have no problem using it.
Flash and ghost are used for a power feed on your lane early game!While in defending build u will need to have the following things:
A champion with a powerful cc such as ryze alistar or maybe caitlynn traps
You to buy 3 health pots a sapphire crystal and rush to ur lane fast.
Start attacking the turret at level 1 while Your enemies will be there be sure that the guy with the cc will be w8ing in the turret when u get low on health or they come to chase after you
start fleeing cast recall while they follow you a few times and move each time they interupt you
this way they will think u r a noob who sucks at some point they will be close to you use ghost to get away and in the end when they will be right behind u and if u flash u will be able to get you near your turret use flash and instantly use rocket grab here comes the time of the cc they should get so they get killed by the damage of turret and your team mate and that way your team get first blood
WARNING: Use health pots while they are chasing u to get some health healed back on u!

Other summoner spells can be used:
Exsaust for another cc
Barrier when you are in Proving grounds

Ones that you should avoid using:
Clarity and heal the enemies will think you have problems with your mana and health and will think you a free kill
Smite some have used to play jungling as blitzcrank but i dont think it is very good!You can try it out if you want though.

Late game you will be able to use your ultimate to kill big groups of minions because its cooldown will be like 18-20 seconds with all that cooldown reduction!

His passive will give him a shield for 50% of blitzcrank's mana when he gets low on health and remember your ccs
Grab
Knock airbone
AOE damage which is an AOE silence aswell

Pros
3 ccs to help your team with killing the enemies
High amounts of damage for a support
Very increased movement speed with boots and his W
Big defencive skills

Cons
Minions sometimes get in front of the enemy a few seconds b4 you get to pull somebody
Easy to fail a grab
Health drops very easily in early levels!