How in general could I improve my make up?

First of all everything depends on your face. The shape, the skin-tone, your eyes ect.

That being said, I there are a few thing that I find to be fitting to most people.

You want to compliment your face and it's figures when putting makeup on and that means no unnatural colors. Very rarely would I use actual colors.

First of all, clear skin! (to be honest, natural clear skin for me is like an eclipse. Whenever it happens there should be a lot of people looking at me and taking pictures, because this might not happen the next many years) 

BUT concealer and foundation goes a long way!

Next step is to use colors that could be natural for your skin. That means all shades of brown-ish colors, bronze and black and white
A very good platte is the naked palette

If it's to difficult to find or expensive (which I found it to be, to be honest), just get any palette in the same colors.

Then; Smokey eyes. Babies, I cannot stress this enough, smokey eyes are the best way to put on eye-shadow, because of the depth it creates. 

If you don't know how to do it. You can youtube it, and I promise you there will be many videos.
A youtube called Lauren, is very good make-up and also michelle phan (I think that that is how you spell it) as another person suggested.

When trying to do a smokey eyes it is important to remember that one must look at it as a sport. And had it been the picture over me would be an OL-campion, because girl, is it difficult!
Take your time and after 1000 tries (I've gone through it, trust me) you will be very pleased with the outcome.

Tone it up and down for dates and clubbing. If I want to feel use it in school I tend to only put a light brown in the crease of my eye and then put mascara on, just to create a light depth.

To create dept to the rest of your face use a bronzer. Which you can also find tutorials on, on youtube.

All of that being said, you are beautiful without make up.
"beauty is in the eye of the beholder," (don't remember who said it) And we must find the ones who she the most beautiful side of us, when we are the ugliest.

Hope I could help