Wash jars and place in a canner or pot large enough to hold the jars plus at least one inch of water. Put a rack or spacer in the canner between the bottom of the canner and the jars, so the jars do not sit directly on the bottom of the canner.
Fill pot with water, place on burner, and bring to a boil.
Place lids and bands in small pot, cover with water, place on burner, and bring to a simmer.
Meanwhile, bring apple sauce to a boil and then let simmer.
Once sauce is simmering and the water containing the jars is boiling, begin filling jars. Fill jars one at a time.
Fill jar, leaving approx. ¼ inch headspace.
Remove air bubbles by sliding nonmetallic spatula between jar and food, repeating around circumference of jar. If necessary, readjust headroom.
Wipe rim and threads of jar clean with damp cloth to remove any food residue.
Place lid on jar with sealing compound net to rim, and then screw on hand until finger tight.
Remove enough water from the canner to allow for the jar to be placed in the pot without water spilling out of the canner, then place the jar in the canner, on the rack if you are using one else on the spacer.
Repeat for each jar.
When all jars are in the canner full, make sure that the water covers the jars by at least on inch. If it does not, add boiling water.
Place lid on canner and turn heat to medium high.
Bring to boil and process (let boil) for at least ½ hour (at or slightly above sea level).
When time has elapsed, turn off heat and remove canner lid. Once boiling subsides, remove jars without tilting and place them upright on a towel to cool in a draft-free place. Do not retighten bands or test for a seal while jars are hot.
Cool jars undisturbed for 24 hours.
After jars have cooled, check lids for seal by pressing on the center of the lid. If the lid is pulled down and does not flex up of down when pressed, remove the band and slightly lift the jar by the lid. Lids that do not flex and cannot easily be removed with your fingertips have a good seal. Any jars that do not have a good seal should be reprocessed or refrigerated.
Label jars and store in cool, dry, dark place.