The common bile duct passes inferiorly, anterior to the epiploic foramen, where it is anterior to the right edge of the portal vein and on the right side of the hepatic artery.
Well, the gallbladder is a tiny little bag that lives underneath the right lobe of the liver. As you can see here, it's attached via the cystic duct to the common bile duct.
When the stomach and duodenum are full, the gallbladder contracts, forcing bile to pass through the cystic duct to the common bile duct and into the duodenum where it helps in digestion.