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The jars and lids should be sanitized in hot water prior to use. Fill your boiling water canner with water and bring that water to a simmer. Place the glass canning jars in the water so that they are completely submerged and filled with the simmering water. Add your lids, as well.  Do not sanitize the band or ring of the lid in this manner, though. These can be washed in plain hot, soapy water. Do not let the water boil. Remove the cans and lids after a few minutes. Note that only a boiling water canner is recommended for canning sauerkraut. Do not try other canners. Back the raw, cool sauerkraut and brine into the hot jars, leaving about 1/2 inch (1.25 cm) of empty headspace at the top of the jars. Pack the sauerkraut in firmly.  The sauerkraut and pressure inside the jar can expand during the canning process. If you pack the jars too full, you may end up causing them to burst open as the sauerkraut sits in the canner. Use a metal spoon or your hand to tap on the side of the jar, gently removing the air bubbles trapped deep down. If you need to fill up more headspace afterward, add more brine. Wipe the rim of the jar clean with a clean towel or paper towel. Center the lid on top of the mouth of the jar. Screw the band on over the lid as tightly as possible. Use jar tongs to carefully lower each jar into the boiling water canner. Bring the water to a boil and let the jars of sauerkraut process for 20 minutes if using pint (1/2 L) jars or 25 minutes if using quart (L) jars.  Note that the above processing times only apply if you are at an altitude between 0 and 1000 feet (0 and 305 m). If you are at a higher altitude, you will need to adjust the processing time. At an altitude between 1000 and 3000 feet (305 and 914 m), process pint (1/2 L) jars for 25 minutes. Change this to 30 minutes for altitudes between 3000 and 6000 feet (914 and 1830 m) and 35 minutes for those above 6000 feet (1830 m). At an altitude between 1000 and 3000 feet (305 and 914 m), process quart (L) jars for 30 minutes. Change this to 35 minutes for altitudes between 3000 and 6000 feet (914 and 1830 m) and 40 minutes for those above 6000 feet (1830 m). Lift the processed jars out of the canner using jar tongs. Place them gently on soft dish towels and let cool completely, at room temperature, before placing them in long-term storage.  Press down on the center of each lid after 24 hours. If the center moves up and down, the sauerkraut has not been properly canned and you should consume it within a week or so. If the jars are properly sealed, though, you can store them unopened in a dark, cool place for up to 2 to 3 years.

Summary:
Sanitize the jars. Fill the canning jars with cool sauerkraut. Process the jars. Store your canned sauerkraut.