Blitzcrank is a great low-elo champion as his ability to pull an enemy from their team can easily win you fights.

Pros

Hook can single out a target for enemy team to take down and win fights
Has 3 abilities that give CC
Good tankiness with P
Great disruption and peeling

Cons

No mobility
No ranged disengage
Dependent on hook (Q )
Mana hungry early game
Easily poked

Blitzcrank's Passive is great for getting out with just a sliver of health. When it is up, you can use this to bait enemies near your tower while on low health then pulling them in with Q

Blitzcrank's Q is your make or break. Your ability to use this will determine whether you win or not. Read chapter below for more details.

Blitzcrank's W is great for quick positioning to land an easy Q . It can also be used to outrun, dodge skillshots and for extra attack speed to take down towers. Be wary of the slow at the end of the movement speed buff. This make it hard for you to do all of the above so make sure you are in a good position when the slow begins.

Blitzcrank's E is your knockup. This is part of your combo after either you Q or your R [Static Field]. You can also use it to disengage and give time for your bot lane to run. This is also an auto reset so use it for that extra damage with an AA E

Blitzcrank's R is a short AOE silence. Use this to interrupt channels such as Katarina's R , Warwick's R and Rammus' Q

Aftershock synergises extremely well with Blitzcrank's Q after you combo with R and E .
Font of Life is easily activated with your Q and E . Try to let your ADC to get the heal before you use the unused CC.
Conditioning gives great all around tankiness. However, opposing lane is long range/has a lot of poke damage you can opt for or respectively.
Overgrowth gives you extra health to tank through the mid-late game fights.
For that extra CDR for late game, another viable option is going for the Inspiration tree. Choose Biscuit Delivery and Cosmic Insight [icon=Cosmic Insight. The biscuits will keep your mana up in laning phase and the 5% CDR from Cosmic Inishgt

Sorcery Tree:
Manaflow Band helps Blitzcrank's a lot. It helps his early mana costs and gives him the free speells and extra mana back to let him Q more in the laning phase.
Transcendence gives Blitzcrank the extra CDR he needs so he can Q more as his items do not give him a lot of CDR.

Cooldown Reduction is the best choice here for Blitzcrank as the CDR allows for more hooks.
This second shard is a choice between Armour and Magic Resist. Take it according to the opposing lane; magic resist against poke/mage supports (Zyra, Lulu) and go armour against other tank supports.
For the last shard, you will generally be taking health, however, if you are laning against a Brand,Lux etc. take magic resist. Armour can also be used against a full AD team comp.

This is what you will be taking most games for the extra tankiness in lane. However, if you confident that you will hit most hooks or are not against a high damage lane, Ancient Coin can be taken for extra mana and increased gold income.
is the best option on Blitzcrank as it allows for quick roams Mid lane. If Mid lane is not able to be roamed on or you need to stay with your ADC, you can buy a .
Knights Vow is the standard support item as it redirects damage fomr your ADC and it heals you.
Locket is another great option on Blitzcrank for defense and the large shield it porvides.
can be swapped with Locket if you are ahead. Blitzcrank is one of the best abusers of this item as his ult cooldown is lower than all of the other supports in the game. This allows Zeke's to be activated extremely often and is often an excellent second buy when supporting a high AA'ing ADC such as Vayne, Lucian, Kai'Sa.
[icon=Iceborn Gauntlet} is great when you are ahead or can easily land hooks. The extra damage is provides and the large amount of mana is extremely useful on Blitzcrank. This can also be swapped for if the enemy team is full AD.
Redemption is another standard support item that gives Blitzcrank extra mana regen and an AoE heal.
is a great buy due to the CC cleanse/immunity if the enemy team has a lot of CC.
[icon=Righteous Glory} Righteous Glory is good for when the enemy has a lot of mobility. The burst of movement speed and the slow it provides is great for getting picks on the enemy team.
is another option for Righteous Glory is you need that same speed for the entire team.

Success is directly proportional to your ability to hook. This means that if you want to do well on Blitzcrank you have be able to predict your enemy's movements and know where they will be. Do not expect to land 100% of your skillshots. For the first few hooks aim in the direction that the enemy is walking then see where they dodge. Base your future hooks off that and see if you can find a pattern. Common dodging patterns include walking towards you or favouring a side. I cannot help you anymore as each player dodges differently. It is up to you to land your hook and carry your team to victory.

If you cannot hook at all, your best bet is walk up to them with W then E for an easy hook. Although you will get poked down pretty hard and this may be impossible if the enemy has good positioning.

Blitzcrank's combos are pretty simple.

Standard Combo

W Q R E
Use W if you need to get into a good position, otherwise, save it for chasing if needed.

If close to enemy

W E Q R
Same W usage as previous combo. Use your E for a guaranteed Q into an R . If the enemy has a dash, use R Static Feild to make sure they can't escape your E .