Here's a bit of a brain-dump, in no particular order. I'm repeating some things already said here... I won't be citing the first person, but just take this as reinforcement!
Get some good recipes and at least one good basic cookbook. Beware that there are some very pretty cookbooks out there where it's clear that the author never actually tested the recipes. I don't know Joy of Cooking, but our basics are Fanny Farmer (mine) and Meta Given (Mrs.k2002's.) These have basic recipes that have been used for a very long time (The first Fanny Farmer was published in 1896; Meta Given in 1947.) I also strongly recommend Cook's Illustrated and Americas Test Kitchen cookbooks. Although they aren't great on a lot of ethnic foods, the recipes are well tested (Mrs.k2002 is a tester) and very well written. The articles in Cook's Illustrated are great because they talk about the process involved in creating a recipe, including variations that they tried that did or didn't work. They also have good basic technique instructions.
Follow your recipes to the letter to start with. Don't substitute right off -- it takes time to learn what you can and cannot change. Yes, it's ok to replace Perfecto® Pickled Pears with Peter's® Pickled Pears but don't try to replace them with Poached Peaches. (Lots of recipes from product labels specify that company's line of products for everything that they can. It's ok to replace with another brand as long as it really is the same product.)
Along the same lines, measure carefully, at least to start. Part of experience is learning when/how to break the rules, but first you need to learn how to follow the rules. This is true in cooking, baking and pretty much any art form. Nobody starts out as a Rembrandt, they start out by copying Rembrandt and then growing from there.
Invest in quality ingredients. I know that's a bit scary when you're starting out -- who wants to waste good ingredients in the chance that you might make a mistake? The thing is that while good ingredients can't save you from mistakes, no matter how good you are you can't make a good result with bad ingredients. I strongly suggest getting good spices: Penzey's has some great starter assortments. The difference between good spices and cheap ones can be amazing. They may be a bit more expensive, but you may find yourself using less, because they tend to be more potent. I know that when my sons are out and cooking on their own, one of the gifts that we will give them is a collection of Penzey's spices.
Learn how to pick your ingredients, both vegetable and meats. The produce person and butcher at your market can be a great source of information. Don't be afraid to ask them. They can also give you advice about how to store various things. Or how to ripen stuff if you buy it a bit green. Visit your local farmer's market and ask questions there. Everywhere I've gone the vendors have been great and very helpful. They want you to succeed, so you'll come back and buy more. They often have suggestions on how to prepare something as well. Getting a lesson in how to pick, store and ripen avocados is very useful -- it's the difference between an amazing guacamole and mashed green soap. The same applies to just about any fruit or vegetable you might want. It also applies to meat. Knowing how to identify a good cut of meat can make or break a recipe.
Start simple. Pick recipes with just a few steps/ingredients to begin with, then expand.
Don't be afraid of cast iron. I know that some people regard it as hard to use but I've never found it to be that way. Once seasoned, the things are very nearly indestructible and you can now get pre-seasoned ones. Yes, you do clean it, you just don't scrub it down to bare metal. That coating, by the way, is not simply a layer of grease. There's a chemical reaction between the oils used to season it and the metal of the pan. It's actually part of the pan, not some yuck that's going to go rancid on you.
Good knives are important. Sharp knives are even more important. Dull knives are actually less safe than sharp ones. With dull ones you have to use more force and more force means less control. Learn how to properly sharpen your knives.
Don't use your sharp knives on a hard (stone, granite) counter; that will dull them very quickly. Either use a plastic cutting sheet or a wooden cutting board. Despite rumors that go around, wood is not more prone to bacteria than other materials. There are some anti-bacterial properties in wood. If you do keep a wood cutting board, coat it with mineral oil (the food stuff, not the stuff used for painting!) once in a while. It helps prevent stains and makes cleanup easier. Again, not the stuff you get in the paint section -- that's poisonous!
Cooking for one or two people: There are some very good "cooking for two" cookbooks out there (including ATC.) Scaling recipes down can be challenging for even experienced cooks, so try to get recipes that are as close to what you want as you can.
Cooking and baking are different disciplines (I'm not going to get into the art vs science aspects, because each has some of both.) Get started with one first and then move on.
Invest in some honest friends and be prepared to take their input, both negative and positive. Learn to distinguish what may be personal preference with actual issues with your cooking. "I hate tomatoes" isn't very useful; "This is a bit too salty for me" is.
Don't expect perfection. I've been cooking/baking for a long time and still have things come out wrong. Sometimes I know what I did and sometimes I don't. It may be something as subtle as the temperature/humidity in the kitchen, for instance. The advice up-thread to try anything three times is good. If at first you don't succeed, try, try again is good advice.