All right. Two questions: Is it free? and what are it's required specs?
There is a free version that you can play in your browser at www.minecraft.net . Go for it.
If you like it, then buy it for 10 Euros (which is about $13 or $14). Then you'll get ALL future updates and expansions for free, like the huge Halloween update that lets you build portals to hell and jack-o-lantern helmets and other stuff. The full release will also include an adventure mode and tons of other stuff. It's gonna keep growing forever. And there are tons of 3rd party mods and skins and junk too. The price will go up a little at Beta, and up a little at full release. So it's actually a deal to buy it now at Alpha, and get everything else for free. And you get to help fund the development of the coolest game ever, woohoo!
But seriously, go play the free version. Ask us for help if you get stuck. Good luck!