I have tried to use many things to clear wine or fermented beverage. Things like cloth, paper towels and coffee filters, non of these work well, but what is the most effective way to clear out the thick yeast left over and further more, after all the clearing is done, is there anyway to make it more clear?
Using any of those things to filter beer will badly oxidize it and ruin the flavor. I clear beer with time and cold temperature. A couple months at 35F will clear just about any beer. You can also use things like gelatin, Polyclar, or Biofine. If you want to filter you needs kegs and a CO2 setup to push the beer so you can do it in an enclosed manner and not pick up oxygen. Or, there's the old standby of drinking out of a porcelain mug so you can't see it! ;)
Use Cold crashing so the yeast and other undesirables fall out of suspension and to the bottom of the vessel.
Finings is another way clarify and drop out the undesirables from suspension in the fluid.
Then Rack in to a new vessel, you transfer the from one vessel to another gently with a siphon of some description and leave behind the sediment undisturbed.