I first mentioned Battlestar Galactica on HIF back in 2008. Since then, my love and adoration for this show has only grown 10 fold. It's not the best show ever created, but it's easily my personal favorite show. I've probably watched it 8 or 9 times all the way through.
And now, you can stream all 4 seasons online for free over at Peacock! They allow you to watch Battlestar Galactica on your computer device or streamed to a TV with something like a Chromecast without becoming a paying member.
You'll want to start by first watching the Battlestar Galactica mini-series. It's a 3 hour movie, split into two parts, which introduces you to the world where humans and rebel Cylon robots are at war. After a surprise sneak attack eliminates 99.9% of humans, the remaining survivors form a ragtag fleet of vessels, protected by the outdated Battlestar Galactica, and flee through space looking for a new home.
Seriously, don't watch the show without watching the miniseries first! You'll miss a lot of important info if you jump straight into the individual episodes of BSG.
After you watch the miniseries, you're all set to begin the show with season 1! Before long, you'll be cursing out Baltar & Tigh, cheering on Kara Thrace & Apollo, and wondering if Laura Roslin & Admiral Adama will ever share a bunk.