If I get a difficult mark on my filter,I can get it off by breathing on the filter, and then gently polishing it with a lens cleaning tissue. More stubborn marks, usually seawater splashes. I use Vision Express glasses cleaning fluid, sparingly. Then remove it with the tissue. Any residual marks after this I use the breath option.
be careful if you have a stubborn mark. This may contain minute solids, as does seawater when dry. You need to make sure you don't scratch the filter, hence the use of a fluid.
I suspect there are as many cleaning techniques as there are photographers