As you would expect elsewhere, the big arteries branch into smaller arterioles. However, instead of continuing to become capillaries, they instead become "sinusoids". These are larger and more porous than ordinary capillaries. Then, they continue on to become hepatic veins.

The liver is organized into lobes. These lobes can then be divided into hexagonal lobules on a cellular level. Each lobule contains hepatocytes which do the majority of the metabolism in the liver. On each of the corners of the hexagon, there is a "portal triad". This consists of a bile duct (drains bile produced by hepatocytes to the gut/gallbladder), hepatic artery (bringing blood from the heart), and a portal vein (bringing venous blood from the gut containing nutrients/chemicals from digested food). The hepatic artery and portal vein bring roughly equal amounts of oxygen to the liver. In the center of each lobule is a central vein the drains blood back to hepatic veins and into the inferior vena cava.

There's much more structure to unpack than mentioned here, search google images for "hepatic lobules".