How to make abstract /marbled designs on a paper?
There are a variety of techniques to do something called paper marbling, and some of them may suit your needs and materials.

The basics of the process come down to putting something in a painting tray, such as water or a foam (usually shaving cream), adding some paint, and then laying the paper on top to absorb the paint. 

Clean up may involve removing excess materials, and generally allowing the paper to completely dry.

Generally, the paint is mixed with something to help keep it sitting on top of the water, where your paper will be. This Rookie Mag tutorial suggests using a little turpentine. Then you can use some sticks to marble the paint together. The tutorial linked has a special device made, but most demonstrations show someone using a single spare piece of plastic or wood to get it done.

You can get some really neat effects due to the way the oil repels the water. Adding drops of plain water to an area of paint will create a circle of empty space. Add a drop of paint inside it and you'll make a ring. You can repeat this to get as many nested rings as you'd like.

There are an amazing number of tutorials already out there to cover this, and a lot of different methods. If this technique is suitable for you, then you should be able to find a step-by-step guide that walks you through getting this done.

FYI, a similar technique is used for "hydro dipping", a popular way to give a tie dye effect on animal skulls. The concept is the same, and so watching the many tutorial videos about it may help give you some idea of the requirements and capabilities of the technique.