I have rendered deer tallow for soapmaking (although I haven't used it yet).  I put it all in a large stock pot with a lot of water on the stove top and gently heated it until completely melted then poured it through several thicknesses of cheesecloth.  I've heard you can also melt it in the oven or in a crockpot or double boiler.  Heat it gently, don't let it boil.  Also be careful not to spill any over the side when stirring.  It's flammable!  I chilled the solid fat from this first rendering, scraped the remaining debris from the bottom and then did it again, using much less water than I used the first time.  The second filtering I poured into a tall and narrow pitcher.  After it has cooled, this makes it easier to scrape off anything that somehow made it through the cheesecloth because the junk will stick to the bottom of the column of tallow.  Wipe out your pot with a bunch of paper towels while it is still warm for easier clean up.  If your tallow has NO smell, you know you've done a good job and it is ready for soaping.  I store mine in the fridge.  Regular fat is not as hard or as shelf-stable as pure white kidney fat, but I am told it does make wonderful moisturizing soap.