Stick to the recommendation of the manufacturer! Do not use solvents used for cleaning windows, do not use liquids for cleaning eyeglasses. These contain additives which might damage the coating of the optical surfaces of the objective and eyepieces. A highly volatile alcohol to ether mixture (70:30) has been recommended in combination with cotton swabs (but check your manufacturer). Only use lens paper for the removal of excess immersion oil from the 100x oil objective, use cotton and the recommended cleaning fluid for the eyepieces. When using lens paper, do not apply pressure, as dust grains might scratch the surface. Cotton swabs have a large surface area to pick up dirt and dust.
Objectives should not be cleaned excessively, and only when necessary. The cleaning solvents do not only remove fats and oils, but might also soften the lens kit holding the front lens in place. The parts should therefore only be exposed to the solvent as short as possible and the solvent should be volatile and evaporate quickly.
It is best to avoid any problematic situations right from the beginning. During my beginning years of microscopy, I made a permanent mount using Eukitt mounting medium. I was too impatient to wait for the medium to dry. I accidentally rotated my 40x objective right into the liquid mounting medium. I had quite some problems removing the medium from the front lens.
Also take care that the cleaning solvent is compatible with the plastic parts of the microscope, in case you accidentally spill something. In short, follow the directions of the manufacturer.