Think about what the sour cream does in that recipe. Is it a thickener, a topping, or what? You'll need to substitute something in the same category.
Think about what sour cream is and does. It's a fat. It's sour. It's thick, creamy, and smooth. You'll want to match at least some of those.
Depending on the recipe, different aspects will have different importance. Topping strawberries, you might substitute nondairy whipped topping. In mashed potatoes, you might prefer margarine and a little lemon juice or cream of tartar.
Look for nondairy sour cream or nondairy yogurt. These are cultured products made from cashews, rice, soybeans, or other plant matter. You can also make your own:
If what you want is creamy, fatty stuff then consider things like avocado or banana. Coconut milk or coconut cream can work. If you want a good flavor-carrying fat, consider olive oil or red palm oil.
If you want to make baked goods wet and heavy, just use zucchini milk. That is, cut up a zucchini, put a little water in your blender, lean on frappe until it liquefies. Use to replace dairy milk in baking. It tastes like it has a zillion calories, but it doesn't. Bread, muffins, pancakes, biscuits, etc. should all work, though you may have to tinker with the proportions.
If you want to make things tangy, try citrus juice, cream of tartar, or you can actually buy vitamin C powder. Also anything fermented will taste sour. Some people bake with sauerkraut or sourdough in rather odd places.