Quality lens tissue (such as that sold by Kodak), a good lens cleaning fluid, and PROPER TECHNIQUE is the way that I have cleaned my lenses for decades. What is "proper technique"?
First - the goal is to clean the lens (or filter - I would use the very same process) without grinding any dirt/debris into the lens. To me, this absolutely dictates single-use surfaces for anything that touches the lens. That's why I use lens tissues instead of a washable cloth or - particularly - something like a lens pen.
Here are the steps that I use to clean a lens:
1. Use a squeeze-bulb blower to blow any loose dust off the lens. 90% of the time, step #1 is all that is necessary.
2. Take a lens tissue out of the pack. Fold it once, holding only what was the ends of the tissue. You want to be extremely careful to NEVER TOUCH the areas of the lens tissue that will be touching the lens. This will avoid transferring oils from your fingers to the lens.
3. Moisten the folded portion of the lens tissue with a little lens cleaner. You don't want the tissue dripping wet, but it must be damp.
CAUTION: NEVER apply lens cleaner directly to the lens (though it won’t hurt a filter, you don’t want liquid leaking into the lens’ innards).
4. Wipe LIGHTLY across the lens ONCE with the damp tissue. Then either turn it over or fold it so that you can wipe again, but with an unused surface. You can do this as often as needed, as long as you never wipe the lens twice with any surface of the tissue. This prevents scratches. Again, make sure you never touch an area of the tissue that will touch the lens.
5. Ensuring that the lens is actually clean, use a dry tissue, handled the same way as above, to wipe the lens dry. Since you have already removed the dirt, there's no risk of scratching the lens with the dry tissue.
6. Dispose of the used lens tissues in a proper trash receptacle.
That's it in a nutshell. Simple and effective. I've been cleaning my lenses this way for over 40 years, and all of them have pristine glass (and none have ever worn "protective" filters).