Summarize this article:

You'll need to look at the interior of the fish to see if it's finished cooking. To get a peek at the inside of the salmon, use just the tip of a sharp knife to push into it about halfway down. You can use a fork, but they usually do more damage to the salmon, which may mar your presentation. While the fish should be an opaque white, beige, or brown on the outside depending on the cooking method, it should still be a slightly translucent pink in the center. If the center of the salmon is opaque, it's likely overcooked. If the center is completely translucent, it likely needs to cook further. You don't want the salmon to flake. If it flakes, it's likely overcooked and dried out. Instead, the salmon should resist flaking but give way and pull apart into pieces when you press the knife into it. If the salmon is opaque on the outside and slightly translucent on the inside and gives slightly when you poke it, it's likely done. It will still continue to cook for several minutes off the heat, so remove it from the stove, oven, or grill, and allow it to sit for about 5 minutes before serving. Because the salmon continues to cook off the heat, it's okay if you remove when it's slightly under cooked. If you wait until the center is a slightly translucent pink and the fish gives way easily with the fork, it should be perfectly done after it sits.

Summary:
Press the tip of a knife into the thickest part of the salmon. Study the salmon's color. Check to see how easily the fish gives way. Take the salmon off the heat and let it finish cooking for several minutes.