Wash the tomatoes thoroughly. Remove the cores, stems, bruises, and blemishes, then cut the tomatoes into quarters or large chunks.
Place the tomatoes in a large stockpot. Add ¼ to 1 cup water, using only enough to prevent sticking. Bring to a boil over medium-high heat, stirring and crushing the tomatoes occasionally. Simmer until very soft and broken down, about 20 to 30 minutes.
Working in batches, press the cooked tomatoes through a food mill, tomato strainer, or fine colander to remove the skins and seeds. Discard or compost the skins and seeds.
Return the strained tomato juice to the clean stockpot and bring it back to a gentle boil. Measure the amount of finished juice. For each quart of juice, add 1 teaspoon salt, ½ teaspoon onion salt, and ¼ teaspoon celery salt. Simmer for 5 to 10 minutes, stirring occasionally.
Prepare a boiling water bath canner and keep clean jars hot. Add 2 tablespoons bottled lemon juice to each quart jar or 1 tablespoon bottled lemon juice to each pint jar. Citric acid may be used instead, using ½ teaspoon per quart or ¼ teaspoon per pint.
Ladle the hot tomato juice into the jars, leaving ½-inch headspace. Wipe the rims clean, center the lids, and apply the bands until fingertip tight.
Process the jars in a boiling water bath canner. Process pints for 35 minutes and quarts for 40 minutes at elevations up to 1,000 feet. Increase the processing time according to the elevation chart in the notes.
Turn off the heat, remove the canner lid, and leave the jars in the water for 5 minutes. Remove the jars without tilting and cool undisturbed for 12 to 24 hours. Check the seals, remove the bands, label, and store.