What's the best way to clean a lens filter?
I bought a used lens that came with a filter. The lens is in great shape but the filter clearly has smudges and streaks across the front.
Am I better off buying a new filter?
What I do is get some lens cleaning fluid, put some on a lint free cloth and wipe the filter. Then I use a microfiber cloth to get any smears off. B&H has an extensive blog post showing how to clean a filter and lens with the tools you'll need.
Always do a non-abrasive cleaning (like a blower brush) before moving on to wet cleaners! If there's a bit of sand or other hard dirt on the filter, scrubbing it may scratch the filter (or lens) perhaps requiring a replacement. A quick pass with a blower will take care of that problem (and perhaps give all of the cleaning required), then you can decide how to proceed with a wet cleaning.
Use dish-washing gel to clean your filters.
I use a microfiber cloth for minor cleaning, and a cleaning fluid (I can't remember what brand, but it's just highly purified alcohol) with PEC-Pads. What ever you use remember two things- if you're using a fluid, always put in on the cloth, not on the glass (this really only applies to lenses, but it's good to get in the habit) and always rub in a circular motion.
Microfiber cloth and drugstore rubbing alcohol. Wipe gently in a circular motion. Air dry.
As you can see, everyone seems to have their own method.