Recently, when posting tips on how to cook without recipes, I suggested learning one or two techniques for each ingredient that you cook most frequently. Just as a guide, here are the techniques I’ve identified for my own personal cooking. These suggestions will give you a place to get started, especially if you’re just learning how to cook. I’ve linked to specific instructions if they were posted previously on my blog.
Please note: These suggestions do not represent every possible way you can cook an ingredient, just the methods that I like best and use most frequently. Also, not all ingredients are listed, because I don’t eat everything. Substitutions are noted when applicable.
Apples: raw in salads or applesauce
Asparagus: pan-roast
Avocados: raw in salads
Bacon: pan-fry or roast
Beans, lentils and peas (dried): simmer in the slow cooker
Berries: puree (especially frozen) to mix in yogurt, oatmeal, smoothies or for sorbets and popsicles
Broccoli: blanch for salads or crudites; otherwise, braise; substitute broccoli rabe or cauliflower
Cabbage: raw in salads or braise; substitute brussels sprouts (cooked)
Carrots: raw in salads, braise or glaze; substitute beets, parsnips or turnips (cooked)
Chicken: grill, pan-fry (cutlets), pan-roast (boneless breasts) or roast (bone-in pieces); substitute shrimp or scallops for boneless breasts
Clams and Mussels: steam
Cucumbers: pickle or raw in salads
Edamame: boil or simmer; substitute fava beans or lima beans
Eggplant: grill or roast
Eggs: bake, boil, fry, poach or scramble
Fish: pan-fry (thin fillets), pan-sear (thick fillets and steaks) or poach (especially salmon)
Garlic: roast
Grains: boil or pilaf
Green beans: simmer
Greens (chard, collards, kale, etc.): boil or wilt in bacon fat
Mushrooms: roast or saute
Onions: caramelize, glaze (pearl onions) or grill
Pasta: boil, pilaf (orzo) or risotto-style
Peas (including sugar snap and snow peas): boil or stir-fry
Peppers: roast
Potatoes: bake (russets), mash (Yukon gold), pan-fry (diced or sliced) or roast (red or new)
Rice: boil, pilaf or stir-fry (leftover cooked rice)
Sausage: grill, roast or saute
Spinach: wilt
Sweet potatoes: bake, hash browns or mash
Tomatoes: raw in salads, roast or saute (cherry tomatoes)
Winter squash: roast or simmer; substitute celeriac, pumpkin or rutabaga
Zucchini: grill or saute; substitute summer squash

This is a great go-to list!
I love the idea of a favorite-methods-by-ingredient list; yours gave me some fresh ideas for veggies. You’ve also inspired me to start keeping my own list!
That’s great, Lelia!