A can of compressed air does wonders; just be sure to spray with enough distance not to damage your art. And you definitely want to avoid using paper towels on your artwork because they can be abrasive. Stick to lint-free cloth (an eyeglass cleaning cloth does the trick) when the need arises, and if you're really of the careful sort, wear clean cotton gloves when handling/moving your art while cleaning (your fingertips leave an oily residue that can damage art surfaces). More great tips here about caring and handling artwork here.
So you've made your first art acquisition, and you're proudly displaying your painting or sculpture like your name was Charles Saatchi. But what about keeping your art clean in your home? Unlike a gallery or museum, we live, eat and sleep in the same spaces where we display our art, and that means a lot of dust.