The below is what I consider the bare minimum for a working kitchen. While other tools will make your life much, much easier, if you have these items in your kitchen, you can make a meal.
large & medium saucepans
large skillet/sautee pan
butcher knife – cuts meat and vegetables easily
paring knife – handles fine knife work and peeling
roasting pan or pyrex dish (at least 9″x9″)
metal cookie sheet
wooden cutting board*
strainer – can’t cook pasta without it and it’s essential to rinse rice before cooking
large mixing bowl
measuring cups & spoons
spatula (I was on the fence about this one. Technically, you can use the wooden spoon for almost everything you’d use a spatula for, but it would be really tough to flip an egg with a wooden spoon.)
*I prefer wooden cutting boards because they’re made of natural material and knives don’t skip off of them. That said, the material is dealer’s choice. Just make sure the bottom grips the counter and your knife doesn’t slide around on the surface.
**My boyfriend will tell you that you can just use a mason jar or drinking glass. He’s wrong. Get a rolling pin.