I attempted to dust the screen of my tv with a cotton cloth and much dust collected in the edges and corners. How can I dust more efficiently as to avoid this build-up?
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.
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.