1. Blow any lose surface grit away with a blower and/or brush
2. I use a squir of window cleaner (from a mini atomiser) sprayed directly onto the filter;
3. Use a clean (make sure!) microfibre cloth to wipe and polish up

For really filthy filters, warm soapy water even dishwashing detergent and water, or liquid soap, and rubbing with thumb and index filter will clean up.
Dry with paper towel.

Some POL filters have very sensitive front glass that scratches easily. In my experience POL filters by Canon are the worst in this regard. No problems at all with B+W, or Hoya but I never use Canon filters (only their cameras!!).

Proprietary lens cleaning fluid could be anything at all and often smears, creating a worse mess to clean up. Out in the field, blowing on the filter and cleaning with a mf cloth is fine. I wouldn't be too paranoid about how to treat modern-day filters: they are are tough breed and a great investment to prevent potential damage or careless cleaning of front elements.