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You will substitute your hand for the roller. Keep the sticky side facing out.  You will probably only want to wrap it around your hand between 1 1/2 to 2 times. You need just enough so that the tape makes solid contact with itself. This is obviously a method of convenience (how long would you really want a tape roll on your hand anyhow?), so there is no need to use too much at a time. Do not wrap the tape too tightly (you will see why in a moment). The tape should stick to the fabric and roll around your hand as it goes (and this is why you shouldn't wrap it too tight). You can repeat the process as many times as needed, and do so on very short notice.

Summary:
Hold the fingers of your of your hands tight together. Wrap your hand in adhesive tape. Run your hand over the lint-covered clothes. Discard of the tape when it becomes covered in lint.