The very first thing a beginner should do when wanting to learn how to paint abstract art is to view and study abstract art and artists that you admire. Pay attention to the color schemes that they used, the brush strokes and other techniques, the type of paint, support, etc. Watch many demonstrations of abstract painting and paint along. Practice every day and eventually you will begin to develop your own style, your own color preferences, brush strokes, compositions, etc. There are no shortcuts.
One method I like to use for abstract painting is a spontaneous type of painting where I will turn on some music, grab a few colors, brushes and canvas and just paint without thinking. I just allow the music and the particular mood that I am in to guide my brush. I have found that the best abstract art is that which was created with a great deal of emotion and passion behind it and with very little planning. One only has to look at the work of Jackson Pollock to understand this.
Below are a handful of abstract painting demos that I hand picked from youtube. I hope you find these helpful and they motivate and inspire you to create your own masterpieces!