I am very particular about cleaning my lenses. First, I never touch them with my hands if I can help it. Second, I use keyboard air cannisters (lower pressure than compressed air which could shoot something into the lenses) to clear off any dust or debris. If you have something stubborn like mud, etc I would use running water the gently break down the mud before using force. Next, I will brush off the lenses with a clean lens pen or similar. If needed I will then gently use a zeiss lense wipe with small circular patterns and quickly follow up with a microfiber lens cleaner. If there are smudges that are still on the lenses, I will use the lens pen cleaning tip side (again very gently). I usually verify the cleaning of the lens in daylight so I can see any flaws, smudges in the lens and repeat or touch up if needed.
I know this is a lot of info but this method has worked for me for years on all of my lenses without any issues or scratches.
Once any debris is gone eyeglasses cleaner and a microfiber cloth work very well. The goal is to use something that won’t scratch the lenses or take off the lens coating, so you don’t want to use anything that is abrasive. You can get the cleaner online or from an eye doc