A note about the photos: You may biggify if you would like more detail.
Finally my process for canning tomato sauce: I throw all my tomatoes in my big stainless stockpot. You want stainless so it doesn’t react with the acid of the tomatoes. Aluminum reacts and will give you funny colors and sometimes change the taste a bit. So use stainless or enamel coated. I don’t core, peel, or de-seed my tomatoes at this point. I just make sure there aren’t any green stems (and sometimes I don’t even bother to do that) and I wash them.
I let these cook down until the skins pop open and as I stir the tomatoes they mush down. I try to get all the tomatoes popped open with my spoon before I do anything else with them. This is also when I add things like garlic so it can cook down with the tomatoes.
Then I scoop tomatoes into my Foley food mill and run them through. This pulls the skin and seeds and core out and gives a nice smooth sauce texture. Garlic cloves that have been cooked with the tomatoes run through the mill nicely as well. I let the sauce cook for a while and reduce down until it is a little thicker. When you first sauce them they are usually pretty watery unless you have all paste tomatoes. I usually don’t fuss with specific kinds of tomatoes. I sauce whatever I’ve got. It just means some need to cook down longer than others.
While the sauce cooks down I get my jars sterilized in my water bath canner. This is also the time I add things like basil if I’m doing a sauce that I want lots of flavor.
I scoop sauce into each jar. I always add about a tablespoon of commercial lemon juice concentrate to each jar. This insures that your acid content is high enough to make water bath canning safe. After jars are full (leave about ½ inch head space, or the space from the food to the top of the jar) run a damp towel around the top of the jar. This removes any food that may prevent you lids from sealing.
Put your warmed lids and rings on. Only tighten the rings finger tight. They don’t need to be super tight or you may have jars break. Process in your water bath canner according to the time on your recipe adjusted for your elevation/altitude.
When putting your jars in and out of your canner is when that funny looking jar lifter comes in so handy. I also use a chopstick to fish out my jar lids without burning my fingers off. I wouldn’t mind one of the lid racks or the magnetic lifter but you don’t have to have them. I’ve canned for many years without just fine.
Now that you’ve got your sauce in the jars, lids and rings on, and the jars full of sauce are in the canner, you need to process them. All that means is that you bring your water back to boiling and you boil them for the amount of time specified in your recipe. Don’t forget to adjust your time for your altitude.
When you are done with processing pull them out and let them cool on a towel on the counter. Lids up. When they are cool you can pull your rings off, test your seal, and wash the jars down. Once that is all done label them and store them in your pantry or cupboard.