As a completely self-taught cook, my top tip would be to understand what heat you are using and why. It took me ages to understand the importance of this. Sometimes you need to be over proper high heat (and prepared to watch to ensure the food doesn't burn), and sometimes you need very, very gentle heat. With gas in particular it can be really handy to have a heat diffuser/spreader which goes between the pan and the ring so that the heat is well spread over the base of the pan - otherwise you can get really hot bits even with the smallest flame.
Don't be afraid to use a bit more salt when cooking. Yes, we should all eat less salt, but if you're cooking something from scratch it's already got way less salt than if you'd bought the ready meal version.
Most recipes with spices don't have enough, especially Delia's - she is mostly wonderful but her "spicy" recipes are pants. Learn to do spices by eye, and don't be afraid to add a bit more. As you get more confidence you will find that the only time you need to weigh ingredients, especially for your standard recipes, is when baking.
Shallots are brilliant. They add depth to any recipe that has onions or garlic in it, and they keep for months in a dark cupboard.
A few drops (but only a few drops) of Worcestershire sauce improves almost any savoury dish. And any casserole is improved immensely with half a teaspoon of Marmite. Tomato paste is not about the tomato flavour, it's about the umami, like the other two, so a squeeze of that can't hurt either. (Just maybe add a pinch of sugar since it can be a bit acidic.)
Eggs are hard to cook with because you often can't recover from mistakes. Always have a plan B when cooking with eggs. If I'm making fried eggs and the yolk cracks, I whizz it with a wooden spoon to make a scrambled omelette.