This article discusses the proper materials and cleaning supplies for safely cleaning your stereo speakers, including the enclosures, grilles, speaker cones, and connections.
How to clean your home speakers yourself
Use a clean, lint-free, soft cloth on your speakers, such as a cotton or microfiber cloth. An old cotton t-shirt works well (cut it into usable pieces). Avoid paper towels, as they leave behind small unwanted fibers or particles on surfaces. Also, use two cleaning cloths to clean your speakers (one for wet and one for dry). When wiping away dust, the dry cloth alone should be sufficient. But for anything dirtier, use both.
This is an efficient and effective way to clean your speaker cabinets:
Dampen the wet cloth so that it is slightly damp with your cleaning fluid of choice, then apply it to an inconspicuous area (such as the back of the speaker cabinet, towards the bottom) to test it. If there is no adverse reaction on the surface of the speaker after a few minutes, it is safe to proceed.