Do not rub them.
Unless they are like the bottom of a dustbin, leave well alone. The micro scratches caused by cleaning can have a worse effect on the image than the dust.
In times gone by, before coatings, a mirror would be left to tarnish and give a better image.
If you must clean them, rinse under running water to sluice off the worst, do not rub.
Then let it soak in a very mild detergent for an hour or so, then gently swab with pure cotton balls in one direction, changing often, with no pressure, just it's own weight. Rinse with distilled water.
If there is any persistent debris you can use pure IPA, then rinse as before.
Pollen is the worst offender, tenacious stuff.
If there are many large holes in the silver (aluminium usually) then get them re-coated. With care and a clean salt free atmosphere they can last decades.