Take a soft cotton cloth, and damp it in warm water. Make sure the water is not too hot to use, it should be warm slightly. After dampening the cloth, wring it until the water is rinsed out completely. The piece of cloth should be moist, not wet. Then wrap it around two bigger fingers of your right hand and gradually remove particles off the brush. Do not rub or press cloth on the brush. Instead use the cloth very softly.
Use of masking tape is also an effective way to clean the lint brush. You can start it with tearing off the masking tape up to about two inches, and wrapping it around the two fingers from non-sticky side of it until its two ends are met and stuck to each other. This will form a loop of the tape.
Place your two fingers inside the loop and then gently rub it on the surface of the brush. It will remove all the dust and other particles off the brush. Make sure you rub the brush softly, instead of pressing hard against the surface of the brush, which can damage it.
Sometimes, you may not find the cleaning process of the brush as cost effective. Also, there is a greater risk of damaging the brush while cleaning it. Therefore, it is better if you buy a new brush, instead of investing your time and money cleaning the old one. You will buy a new brush if the old one is damaged during the cleaning process. Given the level of care that it gives to your clothes and other things, it is not too costly choice to buy a new brush.