Several approaches, all complimentary:
Cook. Start with your favorite dishes. Play with them.
Eat. Go to new restaurants, read menus closely, explore different cuisines.
Learn about food. Go shopping. Read labels. Take a tour of the entire market and see what's there. Go to a farmer's market. Smell the food. Find out what makes ingredients ripe or fresh.
Read. Get one good cookbook. It doesn't have to be comprehensive, just pick your favorite cuisine or whatever looks nice. You could even just read a website online. The key is to pick, say, 5 recipes and follow them start to finish. Get a feel for the flow of a dish, what ingredients are required, how to prepare them, how long it takes, how the dish is presented.
Watch. Cooking on TV is often unrealistic but it can still be educational. Don't be dazzled by their recipes or knife-skills, just ask yourself, "what are they doing and why?", "could I make that?", "what might I do to that dish differently?"
Fill in holes. No one is completely ignorant about food. Everyone has been eating it for years. Start with the things you don't know and tackle them one by one. Boiling water? Google it. Pasta? Google it. Same for steak, rice, salad, salsa, bread, cookies, stir-fry. There are a million versions of all of these, but once you know how to make one, you know about 75% of the whole deal. The rest is just variation. Do each one as an experiment in learning about food. It won't take long to cover the majority of basics. Maybe half a year if you did one every night.
Build up an arsenal. Cooking is practical. Find one dish you can make for each meal. Omelets for breakfast, check. Pasta with red sauce for lunch, check. Hamburgers for dinner. Cookies for dessert... Branch out from there to a few more staples (oatmeal, pancakes, french toast; potato salad, grilled cheese, cobb salad; steak, chicken, salmon; brownies, custard, cupcakes).
Learn about leftovers. Many great and common dishes are actually just last night's scraps turned into today's lunch. Soups, casseroles, stir-fry, sandwiches, and salads are all ideal receptacles for, basically, whatever is lying around. Knowing how to incorporate random ingredients into a delicious dish is half the fun and often all that is required.
Learn about cuisines. Different cultures have evolved their food practices differently, and yet they share basic components. They all employ starches and breads, vegetables, spices, dairy, proteins... Once you realize that the immense variety of food practices share common characteristics, it will seem much less overwhelming. Specifically, finding out which spices are traditionally grouped in a particular culture will give you a centuries-old guide for foolproof flavor combining. You can still innovate, but the historical flavor clusters and food combinations are time-tested.
Learn how to taste. Good cooks are good at identifying flavor. They can spot sweetness, acid, grease, bitterness, and salt amongst a slough of ingredients. They can pick out individual spices from a complex mix. Once you have this power, your cooking will dramatically change, because you'll be able to steer food where you want it to go. This is essential, because it frees you from recipes and gives you access to the infinite possibilities of the kitchen.
Learn something about science. Ingredients are just biology. Flavor is chemistry. Cooking is physics. Rather than agonizing about cooking times, try to identify the common traits of "done" food. What do they look like when they are first heated, then when they are over-heated. Are they drier, tougher, less colorful? When a cake is ready, it will tell you with its scent, color, texture, and (if you can sneak a bite) taste. Being a food-scientist doesn't mean reading textbooks, but using your own observations and a little general knowledge to make great food consistently.
Learn about nutrition. Food is fuel. It is health. It is medicine. Find out what our bodies seek from food, how taste is connected to nutrition, how cuisines supply needed ingredients, and how different preparations enhance (or damage) nutrition.
Whatever you do, don't be intimidated. Cooking is playing with food. It should be fun, even if it doesn't come out right. Good cooks are constantly learning and adjusting. Great cooks know how to cover-up almost all of their mistakes, and you can learn many of their tips. If something doesn't work, toss it and start over. Or do everything in your power to fix it; you'll see what works and what doesn't.
Realize that very few people actually know anything about cooking. It's about 90% hearsay, imitation, experimentation, custom, habit, and personal preference. But that's enough. There's almost always a "right" answer somewhere, but your cooking repertoire will probably evolve just fine despite it.
A cook is equal parts nurturer, mad-scientist, technician, artist, and however briefly, god. Take steel, earth, heat, and water. Make something delicious.