Use a cloth designed to hold dust, such as micro-fiber. Generally, if you aren't using the right tools for the job, your results will be less than ideal. Flat cotton cloth does not hold dust well. Micro-fiber cloths are designed specifically for this.
For the total package: LCD screen cleaning kits on Amazon, Newegg, Google.
There are other tools designed for removing dust as well, such as feather dusters:
You could "hack" it by using other various cloth and brush-like objects that do a poorer job than things actually designed for cleaning, but it would be better to use proper cleaning products.