Clean the belly with a shallow cut made from the anus to just below the gills. A deep cut can puncture the internal organs and spoil the flavor of the flesh. Remove the organs in one piece, then scrape the dark red strip along the backbone with a fingernail or spoon. If it remains, the fish can taste bitter. Finish by wiping the abdominal cavity with a paper towel; do not rinse raw fish under running water, because splashing can spread bacteria to the sink and nearby surfaces. When you are done, wash your hands, knife, cutting board, and counter with hot, soapy water.
Start the cut just in front of the small opening on the fish’s belly and continue to the point where the gill covers meet. Insert the knife only far enough to cut the skin; a deeper cut can puncture the gallbladder, and leaking bile gives the flesh a bitter taste that washing will not remove. Holding the knife with its tip pointing up and lifting the skin as you cut is the safest approach. Small fish can also be opened with scissors.
Once the belly is open, remove the internal organs as one mass. Insert your fingers from the throat end, break the attachment at the upper end, and pull the mass toward the tail in one motion; removing it piece by piece takes longer and can leave scraps behind. Remove the gills at this stage too, since they are the tissue that spoils fastest and can make the fish taste bitter when cooked. Cut the gills at their two ends with scissors and pull them out. If the fish contains roe and you want to keep it, separate the roe sac at this stage and place it in a separate container.
The thin, dark red strip along the underside of the backbone is kidney tissue and must be removed. If left in place, it gives cooked fish a noticeable bitter, metallic taste and speeds spoilage. A thin membrane covers the strip; first tear it with a fingernail, then scrape the strip along the backbone with the edge of a spoon or your thumbnail. Working under a stream of cold water makes this easier and lets you see whether the cavity is clean.
When cleaning is complete, briefly rinse the abdominal cavity with cold water. Do not leave the fish soaking, as this makes the flesh watery and dilutes its flavor. Do not splash the fish around under running water, since droplets can spread to the counter and nearby surfaces. After rinsing, dry the inside and outside thoroughly with paper towels; dry fish browns in a pan and holds salt better. You can press a paper towel into the cavity and leave it there for a few minutes to absorb any remaining moisture.
Sort the trimmings into two groups. Discard the internal organs and gills in a sealed bag right away; do not leave them in the kitchen. Keep the head and bones, rinse them, and set them aside for fish stock or freeze them. When finished, wash the cutting board, knife, scissors, counter, and sink with hot, soapy water. If you will not cook the cleaned fish right away, keep it in a covered container on the lowest refrigerator shelf. If a fish was cleaned at the fish counter, check it again at home; a gill or the dark strip is often left behind.