COOKING 101: Equipment
Just the basics.
Knives: A few sharp cooking knives for meat, veggies, etc. A small knife if you really need to peel stuff (or a peeler). A bread knife. A carving knife if you do joints.
Frying Pan: I recommend non-stick
Small pan: for soup, rice, veggies
Medium pan: for potatoes, small portions of pasta, small dishes
Large pan: for stews, curries, etc.
Grater: For cheese/carrots
EDIT: Forgot some
A grill: handy
An oven: essential
A microwave: handy for warming up yesterday's cooking
Fish slice: for frying stuff (think of the thing you flip omelettes/pancakes with)
Big wooden/plastic spoon: for stirring stuff
Next installment: essential ingredients.
Allow me to post an alternative list, that is both better and more cost effective.
A large carbon steel wok: Cheap, will last the rest of your life if cared for, and is by far the most versatile piece of cookware. You can use it for boiling, pan frying, deep frying, steaming, braising, sauteeing, and just about any other stove-top cooking method you can think of. You can get a large carbon steel wok for $30 that will last longer, and do the entire job of, a whole set of pans.
A large cast iron skillet: Cheap, will last the rest of your life if cared for, retains and distributes heat beautifully, can be placed in the oven.
A large pot: for boiling water. Quality doesn't matter at all, nor does material.
Those are the only real essentials as far as pots and pans go. Buy a small non-stick pan if you like to make lots of omelets, otherwise there is little point in non-stick. In fact, using non-stick cookware severely limits your ability to make a huge range of sauces.
For knives, just get one big one, one medium one, one paring knife, and a steel. Use the steel before and after you use the knives to keep them in fantastic shape. A paring knife makes a huge number of kitchen gadgets unnecessary.
Get some wooden spoons, one heat-proof rubber spatula, and one metal spatula (doesn't have to be a fish slice strictly speaking). Get two big cutting boards.
Buy other gadgets as your needs require (e.g. grater, potato peeler, etc.)
Obviously there's other stuff you might need in specific contexts, and I'm probably forgetting a couple things, but thats a decent essentials guide. The main point is that a wok and a skillet will do for $60 what would cost hundreds to duplicate in conventional pans and non-stick stuff of comparable quality, and will LITERALLY LAST A LIFE TIME.
My general problems tend to be not knowing when to take something out of the oven. I follow the times the recipes say, but it still doesn't tend to come out well. I sometimes put a toothpick in a cake or bread to check to see if it's finished, but it is still usually either over or undercooked (in which case I put it back in and then it almost always ends up overcooked anyways). I know for a fact my oven is basically unpredictable, but I know people with ovens technically a lot worse than mine that bake well.
Other problems tend to be I over or under stir batters so they end up weird, and I have a hard time putting certain ingredients in at exactly the right times for some recipes (for example, a recipe where you have to temper in something).
Basically, I usually just find myself burning myself, scrambling around the kitchen, making a big mess with the dough or batter I am using and not ending up with anything good to show for it.
A few tips, which may or may not be applicable to you:
1) Get an oven thermometer if you don't already have one to ensure that your oven's thermometer is working accurately.
2) Avoid opening and closing the oven often during cooking.
3) Put a pizza stone in the oven so that it retains heat better when opened and closed.
4) If you're having issues with baking that involves yeast, a beginner mistake is using too hot or too cold of water in the proof stage.
5) For cakes and whatnot, make sure you're using good cookbooks, and be sure to follow recipes exactly. Baking is much more precise than cooking.
6) If you're having issues where a bread or cake is rapidly approaching doneness on the outside but still needs time on the inside, put a foil tent over the top to buy yourself some time.
maybe a bit advanced for some 
