Note that EA is only giving the game away for free for a limited time, so don’t take too long to decide if you want to play it or not. You can download it first and play later if you can’t commit any time right now. As Polygon points out, this is actually the second time that EA has given away Mass Effect 2.
The last time they did it was back in December last year. If you’d like to take advantage of the free download, all you’ll need is an Origin account and you’re good to go. The game is normally priced at $20 for the standard edition, and $30 for the Deluxe edition that comes with a soundtrack, digital comic, art book, and various bonuses.
In the meantime BioWare has confirmed that Mass Effect: Andromeda will be released on the 21st of March, 2017, so maybe some Mass Effect 2 gaming sessions will tide you over until then.