The style focuses heavily on upgrades, slowing down the lair to get +1 +1 before your opponent and protecting yourself from timing pushes with roaches, queens, lings and hydras if they are available, before crushing your opponent with a wave of strong +2 +2 roach hydra ling.
The build
It is a fairly standard Build Order :
9 Overlord
15 Hatch
16 Pool
17 Gas
17 OV
@100% Pool : get 4 lings + 2 queens to defend reaper pressure
@100% gas : get speed and pull out.
24 OV
Get another queen at the nat to start creep spread.
32 OV
I usually hit the supply cap at 44 and get two extra geyser and resuming the mining in the first one (so 3 gases)
Get an OV and put down 2 evos and a roach warren, then your third ASAP
Start +1 +1 as soon as possible (and then Lair) so you can start +2 +2 when Lair finishes.
You can then get 4-5 roaches to defend hellion pressure and use your lings to check the Terran's tech and positionning as well as his 3rd base timing.
If you couldn't scout the T's base, putting a spore in your mineral lines is a good idea aswell at this point, as banshees tend to arrive.
@100% Lair : put down hydra den and start +2 +2. Take all gases available. Your creepspread should be pushing far enough on the map to see your opponent's pushes.
Get OV speed and a few overseers, get a good read on your opponent's position and push. Your goal here is to kill one of the bases of the terran. You should have an upgrad advantage and a healthy army, so don't be afraid of a PF. If you manage to kill a lot of his army, don't be afraid to replenish with lings, as they act as great cannon fodder when you're pushing back the Terran's army.
If you manage to kill one of his bases : the game is pretty much won : expand and tech to hive, to unlock vipers and ultras. If you didn't, but killed a fair part of the T's army, expand and tech to hive aswell. If you didn't kill anything, expand and get a big army.
How do I deal with :
Mech :
Two choices : you know his army position : go around it and destroy an unprotected base. Losing an army vs mech is annoying, but if he loses a base or even better some production structures if you manage to go in the main, that's great.
If you can't go around his army, quickly tech to hive and expand a lot (try to be 2 bases ahead of him). Use vipers to blinding cloud, and kill his army. If you can kill his army, the game is won. Just go and wreak havoc in his bases. Otherwise, go for the ultra transition, get more queens and play roach hydra ultra queen vipers.
Mines / Hellbats:
Mines are great, cause they suck vs roach hydra. Get a few overseer with speed and use them to detonate mines over the terran army. Win the game. (this is only easily done if you have an upgrade advantage over the Terran)
Same goes for hellbats timing pushes, they straigth up die vs roaches queen hydras, and you can go and chase them down for the win. Plus early hellbat pressure usually puts T behind you economy wise (if you defend well).
Marine Marauder Tank :
This one can be tough, you need to assess the tank numbers and medivac numbers as well as the army size. If there are too many tanks, fall back and get vipers. You can try to go around aswell, as tanks slow down a terran army.
Otherwise, push in and use a small chunk of army to focus down tanks.
That's about it.
A few links to replays (please ignore the fact that I suck at sc2) :
http://sc2replaystats.com/replay/2001858
http://sc2replaystats.com/replay/2001899
http://sc2replaystats.com/replay/2001897
http://sc2replaystats.com/replay/2001895
EDIT: Hyun vs Fantasy (WCS Tiebreaker) Game 4