Whether you're just getting into makeup now, or feel you have certain areas to improve in, the most important place to start is understanding your skin type, and working with it, rather than against it. This is where most people go wrong, so as long as you have this down, you shouldn't have any major problems in the future with your technique.
Oily skin will look shiny and greasy, almost as if you have just had a workout and you start to sweat, mostly leaving obvious traces around your forehead, nose, and cheeks.
Because of the excess oil, you may experience a lot more acne than others, along with larger, more visible pores, so it's very important to keep your face clean as much as possible, and avoid any creams that contain oily ingredients (like coconut oil.) You may even want to carry around some antibacterial wipes with you, so you can have a quick clean up whenever you need to when makeup is a no go.
Makeup wise, the key is a gentle toner that will remove any excess oil and dirt, you can find many options to choose from on the internet. Then choose a water based foundation as this won't be packed full of unnecessary oils. An absolute must have is powder, so when going in to contour, use a powder to sculpt out the cheekbones and slim down the nose (instead of a cream), and always remember to set your face with a good quality translucent powder. In fact, keep it with you whenever you head out, and as soon as you feel a build up of oil, just pat on the powder, and you will be as good as new.
Dry skin will feel tight, flaky and even powdery within minutes of getting out of the shower or just after you have washed your face. This will be because your cells underneath your skin aren't making enough oil glands to hydrate itself, and because it lacks moisture, it will be your job to make sure it's getting enough. You can do this by investing in some top skincare products that not only moisturize, but they stimulate those glands to work again, that way your skin isn't having to rely on the cream - it has to work for it.
You will want to choose the right kind of foundation too; otherwise it will dry out and look as if it's crumbling in certain areas of your face, (usually around the nose and mouth area.)
You may also want to use face masks on a regular basis. Look out for the ones that include aloe vera and coconut oil - they work best. Just make sure it's natural.
Regardless of the makeup and skincare products you buy - if they aren't suited to your skin type - they won't look good. So always put that first before falling in love with a product, only to realize it makes your skin look and feel even worse.
As soon as you master that, you'll be flawless.