So, what exactly is StarCraft II?
StarCraft II: Wings of Liberty is a military science fiction real-time strategy game. It is made up of three races (Zerg, Protoss, and Terran).
Click for more information


Heart of the Swarm (expansion)
Heart of the Swarm expansion adds better matchmaking, advanced social features, new units, and a sweeping cinematic campaign.
Starcraft II: Heart of the Swarm Expansion


Gameplay overview
Below is a link to a video, explanation, and screenshots of the basic gameplay of Starcraft.
Gameplay overview


Battle.net
Starcraft II uses Battle.net as it's online gaming service. You use your Battle.net account to log in to the game which lets you use Battle.net’s leagues and ladders for online ranking.
Battle.net sign up


Competition and ranking
Starcraft II has a very high level competitive aspect. It's a huge part of e-sports and has many high level events from the e-Sports League (ESL), Starcraft 2 Pro League (SPL) and World Championship Series (WCS). Besides these there are ranked ladders with different levels: Bronze, Silver, Gold, Platinum, Diamond, Master, and Grandmaster.


Casual and fun
If you're taking a break from laddering or just don't too much competition, you can host custom games with your friends or against multi-leveled AI. There are also arcade type games and and gimmick game/mods with new ones being added all the time. All of these can be done and played in-game.


Buying Starcraft II
You can buy both Wings of Liberty and the Heart of the Swarm expansion straight from Battle.net. I would recommend buying the bundle of both together to get the discount. There are also some really good deals on bundles for the two if you just do a quick google search. It makes it cheaper. It's really not much considering the replayability of Starcraft II and the fact that it is the longest running game franchise ever (longer than Diablo II). A once of purchase of the game is less than someone would spend on LoL within a few months.
Buy Starcraft II (link to the bundled deal is on the page near the right)


Try it for free
You can try the game out for free. Though this only gives you 5 missions at the start of the Wings of Liberty campaign (single player) as well as some multiplayer games (no laddering). You still need a Battle.net account to try the free version.
Try it for free


Screenshots

marines > zerg, get over it

RP Chat > Starcraft II

YGO > LoL+Starcraft 2

(I play LoL too xd)

Starcraft II Global Finals (top 16 players throughout the World Championship Series) live at Blizzcon

http://www.twitch.tv/wcs

still lookin for a way to get this this game for free...

There's a heading in the opening post entitled 'Trying it for free'. Take a look. But the free to play is limited. It's a purchased game for the full version, but it's also a once off pay and never again.