Core and Score
Using a small paring knife, cut out the tough core of the tomato, then score the bottom.
Blanch and Shock
Set a large pot of water to boil; keep a cooler full of ice water nearby. Submerge the tomatoes in boiling water for 20 to 30 seconds, until the skins wrinkle and split. Remove them to the ice water. Depending on how many tomatoes you are processing, you may need several changes of ice water, as the hot tomatoes will quickly melt the ice.
Skin, Seed and Crush
Set up a workstation with three positions: A large bowl or pot, another large bowl or pot with a sieve over it, and a pot large enough to capture the tomato pulp for cooking. Remove each tomato from the ice bath. Peel the skin away and cast that into the first bowl or pot. Over the sieve in the second bowl or pot, tear open the tomatoes and remove the seeds and liquid from the chambers. Move to the third pot and crush the tomato pulp with your hands in it. This is where it will be most apparent whether tomatoes are too under-ripe, as the skins will not want to come away, and the fruit will be too hard to open and crush.
Using a spatula, massage the seeds in the sieve to extract the water. The seeds will retain some gelatinous exterior. Discard the skins and seeds, reserving the tomato water. This can be used much in the same way as a stock, e.g., a base for soups or braises, and is very flavorful.
Alternatives: For a puree, place tomato pulp into a food mill over the third pot, and puree it into the pot. For tomato juice, place skinned tomatoes (with seeds) into a food mill over the third pot (no second pot necessary in this case) and puree.
Place the pots of your crushed tomatoes (or puree) and water on the stove. Bring to a low boil and reduce heat. Simmer the crushed tomatoes until they break down.
Meanwhile, have your pressure canner filled to the 3-quart line and over a high flame.