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.
You'll want to first start by watching the Battlestar Galactica mini-series. It was a 3 hour movie, split into two part, that was so popular they spun it off into a show. Seriously, don't watch the show without starting here first. You'll miss a lot of important info if you jump straight into the show.
After you watch the mini-series, you're all set to begin the show with season 1! They're listed in backwards order, so you'll need to scroll to the bottom to find the first episode.1