Well, either you can sign up with a Minecraft server hoster, or you can just download the minecraft server jar from the Minecraft website, run that and forward port 25565 to your computer in your router.
It's possible, but I wouldn't recommend it. You'd be better off finding a company who specialises in Minecraft server hosting.
Of course, if you do need to host it from a VPS, you could probably get it working by just installing java on there and running the minecraft server jar. I'd recommend using bukkit and some mods though to prevent griefers etc.