How do I actually get the game to play it? Or is it only available to a select few?
Neither the Infinity MMO nor Infinity: Battlescape currently exist at the moment. You can’t “get” either.
I don’t know who told you that you could, but I think you were being mislead.
Get it to play? That implies you have it installed. Are you trying to run the ICP (Infinity Combat Prototype), perhaps? The ICP was a proof of concept released years ago to the community to test networking code. Neither the official ICP server, nor any of the community hosted ICP servers are currently online. If you’ve managed to get your hands on the ICP, it should include the server executable. You can run your own private server with that.
We’re working on launching a Kickstarter to fund the development of the game within the next few months. We’re also working on releasing a demo immediately prior to launching the Kickstarter and that will be publicly available.