Look at more abstract paintings. Not all of it takes the same approach; some is more what I would call formalist, some is more expressive, lots in between. Non-objective art is usually included in the larger umbrella of abstraction, but so heavily abstracted that it doesn't start from an objective reference point. Art history and criticism can also provide some useful context, so don't be afraid of reading that stuff.
The other thing to do is what everyone has already mentioned, which is learn all the formal elements that go into art. Shape, composition, and color theory. I was personally only able to comfortably create abstract work after many years of schooling. The main issue I had was weaning myself off an impulse to illustrate in a more literal sense. Once I was able to start seeing a figure as just shapes, rather than eyes, nose, legs, etc. it got a lot easier to do abstract work. Because I wasn't thinking "what is the message I am communicating?" or "how do I convey that this form is a person?", I could focus instead on pure form, the feeling of a line, etc.
On this particular work it's all about layers. Every colour looks like it was left to dry before using a palette knife to add more, which means that the blue catches on the texture left behind by the yellow, instead of just mixing on the painting surface.
But yes in order to make a proper "abstract" painting and not just a fancy texture it does need thought and composition and such that others have suggested.
See, the thing is that in good non-representational art, the shapes and colours are not random. You still need to know all the theory behind visual design, you just get to skip the part where you make the painting look like an object. So of course if you don't know the principles of design and how to put them together, you will have a mess.
You should probably start by finding some books/tutorials on composition. Also, look up the principles of design on Google so that you know what you'll need to keep in mind while trying to paint.