If there is a harder particle or smudges on the lens, you need to use an optical lens cleaner to remove smudges and other dirt. Despite using an alcohol base, lens cleaners are safe to use as long as they come from a reputable company. Lens cleaners mainly use isopropyl alcohol solutions mixed with mild soap and water, which when applied carefully will remove any stubborn dirt, debris or lingering stains.
Do not spray the cleaner directly on the lens, as this more easily damages the coating. Instead, spray the solution on the cloth, then thoroughly clean the front element of your lens with it in circular motions outward from the center.
If possible, avoid cleaning the rear lens unless absolutely necessary. In over 18 years of professional photography, I have NEVER had to clean the back element of a lens with a lens cleaner. Being so close to the sensor inside the camera, this part of the lens is crucial and therefore needs to be heavily protected. Try to avoid any type of wet cleaning solution, if possible. In my experience, prevention is better than cure, so I have always been extremely careful with the back element of my lenses.
While you’re at it, get out some cotton swabs, spray the solution on the tips, and quickly clean the lens contacts. This removes dirt, grime, dust, and anything else that can impede communication between camera and lens.