First you need to have an imagination and basic painting supplies.
I would suggest getting pre-stretched and primed art canvas.
The general idea behind this method is using masking tape to tape off perfect squares, circles, outlines, and triangles to make a cool picture.
Start with one basic shape somewhere around the middle of the canvas. I would suggest a square with a light brown color.
Its very simple from here. Just tape off the shape you want and paint in the spaces. Its almost as easy as paint by numbers.
Stick to the easy stuff. If you get fancy, your painting will look like crap. You want to pick out a max of 5 colors at the beginning. Make sure all of the colors are neutral. I would say a red, brown, and black are a must.
From here just make shapes and paint them in. Remove the tape, let the paint dry just a tad, retape another shape, and rinse and repeat.
There you go. You now know a simple way to paint some abstract art. Have fun.