The decoration of fabric has many different ways it can be done. A few examples are: dying the threads, using already differently colored material, painting, screen printing, embroidery, weaving, etc. You should ask a more specific question because fabric patterns have a rich history in just about every culture and spans thousands of years.
There are a lot of different ways to get fabric patterns. Some simpler patterns can be woven on a loom using different colored threads. Other patterns can be embroidered on plain cloth after it is woven. Today, a lot of patterns are prints, which basically is just an inkjet printer that prints fabric dye onto plain fabric.
Patterns are designed by people, hand drawn or created on a computer using an art program.
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