Sterilize canning jars, and prepare two-piece canning lids according to manufacturer’s instructions.. Sort and wash fully ripe peaches. Remove stems, skins and pits. Crush peaches and put into a large pot with the water.. Over medium heat, cook gently for 10 minutes. Add sugar and slowly bring to a boil, stirring occasionally until sugar dissolves. Cook rapidly until thick, about 15 minutes, stirring frequently to prevent sticking.. Pour hot jam into jars, leaving ¼-inch headspace. Wipe jar rims and adjust lids.. Process in a boiling water canner, following manufacturer’s instructions. The recommended process time for peach jam in a boiling water canner is 5 minutes for half-pint or pint jars.