With the grand old Galactica crippled from the final jump, the survivors’ only choice was to settle wherever Starbuck had landed them.
The notes gave her the coordinates for Earth, and she was able to jump them to safety from the exploding Cylon ship.
The fleet had just enough juice left that what was left of Sam Anders was able to pilot the ships into the sun.
The colony survivors ended up on this new Earth thanks to Kara suddenly realizing the meaning of the tune that would become “All Along The Watchtower.”