Currently I use Greater Mark of Magic Penetration to make Static Field a little bit stronger, Greater Seal of Armor to be tougher early game, Greater Glyph of Cooldown Reduction to reduce cooldowns late game and Greater Quintessence of Health to be tanky early game.

Rocket Grab
Blitzcrank fires his right hand, if it encounters an enemy unit it will stun them and deal 60 / 120 / 180 / 240 / 300 (+80% of ability power) magic damage while he pulls them to himself.

Cooldown 22 / 21 / 20 / 19 / 18seconds
Cost 140mana
Range 10000

Is your number one killing tool. There is no need to stack Abilty Power or Cooldown Reduction for it. Rocket Grab plays on one of the most important factors of League of Legends: crowd control, in my opinion this is one of the largest, most invasive skillshot. it is best used around towers, either to pull the enemy out their turret or to pull him into your turret. This is very effective after retreating to the safety your turret to lunch a quick grab to damage the enemy so they have to recall as well.

Overdrive
Blitzcrank super charges himself to increase Movement Speed by 16 / 20 / 24 / 28 / 32% and attack speed by 30 / 38 / 46 / 54 / 62% for 8 seconds. However, when this effect ends his movement speed is decreased by 25% for 3 seconds.

Cooldown 22seconds
Cost 90mana
Range 1

A straightforward ability. It makes you excellent at escaping cretin death . It boosts movement speed as well as attack speed. This ability removes any need for pure attack speed items.

Power Fist
Blitzcrank charges up his fist to make his next attack deal double his total attack damage and pop his target up in the air.

Cooldown 9 / 8 / 7 / 6 / 5seconds
Cost 25mana
Range 300

Looks as a plain ability, but however it refreshes the auto-attack and knocks the enemy up in the air. Therefor it's beneficial to use Power First right after an auto-attack. Power Fist is most effective after Rocket Grab because no only is the enemy caught off guard they are also demobilized for a second.

Static Field
Passive: Lightning arcs off of Blitzcrank to hit a random nearby enemy for 100 / 200 / 300 (+25% of ability power) magic damage every 2.5 seconds.

Active: Deals 250 / 375 / 500 (+100% of ability power) and silences surrounding enemy units for 0.5 seconds. The passive is not in effect during the cooldown.

Cooldown 40seconds
Cost 150mana
Range 600

Using your Static Field right after you pull someone into your team is useful because they are silenced and won't be able to use abilities to escape. With a tanky focus on Blitzcrank your Ult will still do damage but don't expect massive devastation to come from it. Use it for it's silence mainly. Save your ult in fights for times where silencing whoever is around can turn the tides or save your team. Even when you don't use your ult the lighting strikes deal some damage for even more reason to save your ult for a later moment.
As far as ultimates go the its passive is very helpful in farming.

I tend to use Heal and Ghost

because after retreating to your turret it can be used to pick up an kill early game when the turret is still dealing a lot of damage. Use Power Fist to knock them up and then Rocket Grab to pull them back into the turret, letting the turret do most of the damage

because this is an excellent escape tool when paired with Overdrive

Starting Item and quickly upgrade to to maximize mana

The Core or depending on who you are laning against
Mercury's Treads if the enemy has multiple stuns.
Ninja Tabi if the enemy team has a lot of physical carries and a lack of crowd control.
Boots of Swiftness, if the enemy team lacks both a good amount of crowd control AND physical carries.
Thornmail should be bought first if dealing with a large amount of lifesteal
Force of Nature if dealing with strong ability power

After the Core
Warmog's Armor is used to make you tanky
Warden's Mail to give you health regen in lane
Manamune to give you all the attack damage you will need

Finishing Touches
Randuin's Omen is used for armor and health regen as well as to slow enemies
Guardian Angel because most teams will mistakenly focus you
Trinity Force to give you a litte more damage