For cleaning the eyepieces, use cotton and not lens paper. For removing immersion oil, you can use lens paper. Do not press too hard when cleaning the surfaces, dust or sand grains may scratch the surface.
Immersion oil should be removed with lens paper after every use, but it is not necessary to dry-wipe the objective. Make sure that you use synthetic immersion oil, which does not solidify over the years. Immersion oil collects dust and this is the real problem.
Always use a dust cover (or put the microscope into a box). The dust can be removed from the body of the device with a moist, but not wet, towel. Do not use solvents or household cleaning fluids on the microscope. And always follow the instructions of the manufacturer.