Soup is not known to be highly acidic, so a hot-water bath canner will not be advisable, and any soup with meat in it must be canned with a Pressure Canner.
A Pressure Canner
A pressure canner is a special type of pot. It has a lid that locks in place, and has a valve that allows pressure to build, up to a certain point, inside the pot. This pressure allows the heat inside the canner to reach 240.F (116.C), which can destroy toxin-producing bacterial spores, and other nasty things that can spoil your food. High acid foods like pickles in vinegar will do fine being processed at 212.F (100.C), but low-acid foods need the extra heat.
If you are planning on getting a Pressure Canner, understand that you need to get one labeled for Canning. A pressure cooker is not the same. A Pressure Canner should come with several valve weights so that you can work with either 10lbs. or 15lbs. PSI. The pounds per square inch will depend on if you are above or below 1000 ft. from sea level. eeech! Sounds complicated, but I am going to recommend that you also buy "Ball Complete Book of Home Preserving" isbn 0-7788-0139-X. There is a mass amount if info in the book, and with the directions that come with your Pressure Canner, you should be fine.
So, you are still here, you have a big ol' pot of soup on the stove and you are ready to get it in the pantry. This part is actually pretty easy. I like to use large mouth quart jars, which is about 4 cups of soup for each quart. Wash as many jars as you will need in hot soapy water, the lids and the rings also. (I always prepare an extra one, just in case I miscalculated) Put the rings and lids in a small sauce pan and put them on low heat, do not boil them, just keep them fairly hot. My pressure canner calls for 3 quarts of water, so I put the water in first, and then set the jars on the bottom rack. You can add a tablespoon or 2 of vinegar to the water to prevent water spots or mineral buildup on your jars and canner. Put the lid on the canner, but don't lock it, and bring the water to a boil. This should heat up your jars just fine. You want the jars hot because if you put hot liquid in cold jars, they can crack and will burst during canning.
Once the jars are heated, I do turn the heat down on the canner to medium, because I don't want to boil all the water out before I get the jars done. So, here is my production line. Soup, peppers, jars, canner. Now with Pepper Steak Soup, the bell peppers can get way over-processed if I add them to the soup and cook them first, so I add about half soup to the jars, then add raw bell peppers to the jars, and then fill up the rest of the jars with the soup. I also only cook the carrots half way, because they will soften during processing. Make sure that you leave a good 1" of head space, so that when the liquid expands, it doesn't blow the lids off. That just makes a HUGE mess, trust me, I know.
After the jars are filled, wipe the rims with a paper towel. If you have meat, use a little vinegar on the paper towel to make sure there is no oil or grease on the rim. Next, take the lids (always use new ones, and throw any used ones away, because the wax is one-use only) and put them on the jars, and then take the rings and screw them down tight, but do not wrench on them. Now just place the jars in your canner, turn up the heat to high, and put the lid on your canner and lock it in place.
All the jars happy in the canner!
The biggest worry now is how to time your soup. The Ball book has a recipe for "Beef in Wine Sauce," and one for "Beef Stew with Veggies," but none for my soup. The book also stresses that you should only use tested recipes, but my soup is not a tested recipe. Well, I go with the closest thing, and err on the safe side and pick the one with the longer processing time. The wine sauce is thin, but the stew is thick. My soup is in-between, so I pick the times for the stew.
Following the directions, I wait for the steam to come out of the open vent , and then count 10 minutes. Once the 10 minutes are up, I put the 10lb pressure control weight on the valve, and count for 90 minutes after pressure is achieved. Pressure is achieved when the little red button on my lid pops up, this varies by Canner, so do read your directions. Once pressure is achieved, you can drop the heat down to med-high or so, just make sure that you do not lose pressure. Now I do stay close, cleaning the kitchen, reading, playing on the computer, and listen for my weight to dance and let off a bit of steam here and there. This is normal, and lets you know you are doing it right. If your weight is not swaying, or dancing, your may be losing pressure, and you may need to turn up the heat. If your weight is going crazy, your heat may be too high. A soft sway, a bit of steam let-off every 3-5 minutes is good. If you do lose pressure (my red button will fall) you have to bring up the pressure and start the count all over again. Do not ignore this, as I did once. I thought "Oh, the pressure only dropped for a minute before I got it back up so I should be fine." Sixteen jars of green beans bubbled, fizzed and stunk up my pantry so bad that I had to pay my son a handsome sum of money to make the problem go away.
Locked, Pressured, and Rocking!
After reading a few chapters, and 90 minutes, I can turn the heat off and let it come down to normal pressure before opening the canner. Once it is a normal pressure, you can open your canner. Do be careful, as the contents will still be extremely hot. Let the jars sit for a few more minutes, and then use a jar lifter to remove them. Place them on a rack to cool. The best part of this process is about to happen: sit back, relax, and listen for the "ffwipT!" of the jar tops. The tops suck in, creating a vacuum top, and this is how you know you have a good seal and you did it right. If a top does not suck down, don't worry, it is not ruined. Just put it in your fridge and have soup for lunch tomorrow.
Once the jars are cool enough to handle, write on the lids what it is, and the date you canned it. Store in a cool, dark place, like a pantry in your basement. Sunlight and heat can ruin the contents. Too much joustling, or tipping the jars over, can break the seal, so be a little more careful than you might be with tinned soups. If all is good, these jars should be fine for a year or two, but I will check the tops every month or so, and if a top pops, (this is where you can push the top down and it bounces back up, indicating air has gotten through the seal) I will sadly toss the contents. Do not worry though, in all the years that I have been canning, I have only had one raspberry jam pop, never a soup. (We do not talk about the green beans)