For those new to eating food that does not contain dairy or meat, here is an excellent article by Jennifer Chen on how to stay true while cooking at home.
There are a ton of vegan cheeses out including shreds, wedges, artisan blocks, and slices, but to achieve a cheesy flavor, nutritional yeast is the way to go. For a little more dimension, Newman and Steen add a little maca powder to the “nooch.” Maca powder is pricey so reserve this method for a special-occasion dish. Coconut milk or cream is great at mimicking a buttery, cheesy flavor when combined with nooch. Cashews are stellar for replicating cheese sauces. Crumbled tofu, flavored with spices and vinegar, are great ways to replace feta, ricotta, and cottage cheese, or make your own Parmesan by pulverizing walnuts and nooch together.