Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
This is just a simple build which requires a fair bit of gold. Lucky for you it is easy to kill mages at lvl 1 :)
The purpose of the large health regen is to help you in running away and to mitigate minion damage, allowing you to farm quickly and reduce the number of deaths.
I have noticed the stats above don't show the +2% of the Atma's in damage or the bonus health from mana. The true figures are around 211 damage and 4.5khp.
I'll probably get criticised for this build but I tried it recently and it works nicely. The build order above is only rough, I'd recommend starting with a Ruby crystal, followed by a Sapphire Crystal, before combining into a Catalyst the Protector. That deals with all the mana you should need early game. Following that, get a Boots of Swiftness, followed by a Blasting Rod and finishing the Rod of Ages. Singed gets a 2.5 health per 10 mana, which means by the time the rod is charged, it will give you 811hp and 725mp. Warmog's is self explanatory - health and health regen increasing with time. Atma's will give you roughly 80-90 damage when your Warmog's is full(around 200 total damage). Spirit Visage for the slight magic res and cooldown reductions(also health regen bonuses) and Nashor's tooth for the cooldown reductions and attack speed. With Insanity Potion you'll be looking at around 1.5attacks/second, 270 damage. I suppose some armor penetration would be nice, but this build was kind of thrown together mid game to see if it worked, and it did.
Oh yeh, At the end game to get some bonuses use The 3 Elixir's to give you around 4.7khp, 270 ability power(after insanity potion) and 1.7 attacks per second(after insanity potion).
The obvious weakness is Madred's Bloodrazor, but in my experience the people who get them are usually squishy, so if your team has someone who can stun, then it is a simple matter of stunning them and finishing them off.
Get Fling first, helps with first blood.
Get Poison Train second and third to help farm.
Get Fling again.
Poison Trail again.
After that get whatever you think may benefit you. Obviously get Insanity potion as soon as you can. You may want to get a Mega Adhesive earlier if you find you are slipping, it can help with catching enemies.
Let the minions follow you through the poison clouds, nothing easier than that. At level 18 with this build(and elixirs, insanity potion) I was doing 200(approx) damage with poison trail. Minions never stood a chance. Also enemies following you tend to die a lot :)
The idea of the huge health is to rush forward and fling the enemy back to your team for a quick kill. If you team with someone with stun and you use ventrillo, get them to stun just as you reach them, so you fling them back and they get stunned which will allow you to capitalise on this.
If you are running away, you can use fling to help you escape, just rush towards them and fling and sometimes they will just go over you and you can keep running(its funny when it happens 5 times in a row to the same guy).
Pros / Cons
Pro: Fast, huge health, good lead character in attacks, excellent boosts with Insanity Potion. Ghost and Insanity potion can get you around 550 speed, enough to catch almost anyone. Flash can also be good to catch an early first kill that would otherwise escape.
Con: Obviously the weakness to Madred's.