I own a DeepCool laptop cooler, and would like to know how to properly clean the fans and mesh grills.

There are a couple of ways to clean a laptop cooler, but the most practical method is to use compressed air and blow out any dust that has accumulated. Other methods, would require the disassembly of the unit, which we wouldn't recommend. Also note, that DeepCool will replace your unit if it develops issues while still under the covered warranty terms.