It used to be that you could simply mush up some raw tomatoes in a mason jar, screw on a lid, process the jar in a pot of boiling water, and that was it - canned tomatoes.
There are a couple of extra steps I recommend nowadays that result in a safer product that also has superior color and taste. The first takes only a second, and is essential to canning tomatoes safely nowadays.
Why you must add acidity to tomatoes before canning them:
Old fashioned tomato varieties had enough natural acidity in them that you could safely can them without adding lemon juice, citric acid, or vinegar. But in recent decades many tomato varieties have been deliberately bred for a sweeter, low-acid flavor. These newer varieties cannot be safely canned in a boiling water bath unless you increase their acidity.
Since I am usually not 100% sure whether the variety I'm canning is considered low-acid or not, I take the precaution of adding the recommended amounts of 1 tablespoon of lemon juice or vinegar, or 1/4 teaspoon of citric acid to each pint jar. Double the amounts if you are using quart jars. I don't really notice a difference in the taste, but if you're worried that it might be too sour, you can add a little sugar to offset the added acidity.
The easiest way to can tomatoes:
The raw pack method is basically just chopped up raw tomatoes smushed into clean jars with added acid as described above (it is not necessary to sterilize the jars for this or any of the other tomato canning methods described here). The tomatoes release enough of their juices to completely cover the pulp.
The only advantage of the raw pack method is less active prep time than if you peel, seed, or lightly cook the tomatoes. The disadvantages are longer processing time and a seedy, watery product that tends to separate once it cools in the jars (the red pulp will float above a layer of almost clear liquid).
You can tell I'm not a fan, but if you do decide to use the raw pack method, be sure to leave at least 1/2-inch head space in the filled jars. Process pints in a boiling water bath for 40 minutes, quarts for 45 minutes.
A better way to can tomatoes:
This method, called hot pack, still skips peeling and seeding the tomatoes, but results in less separation in the final product. Simply core and chop up your tomatoes. Discard the cores. Put the chopped tomatoes into a large pot and bring to a boil, stirring. Boil them for 5 minutes.
Transfer the lightly cooked tomatoes to clean jars, adding acid as described above, and leaving 1/2-inch of head space in the jars. Process in a boiling water bath, 30 minutes for pints, 35 minutes for quarts.
The best way to can tomatoes:
This variation on the hot pack method results in a brightly colored and flavored product that doesn't separate.
Bring a large pot of water to a boil. Cut out the core ends of the tomatoes and discard. Drop the cored tomatoes into the boiling water for just 30 seconds or until the skins start to curl. Remove the tomatoes from the hot water with a slotted spoon.
When the tomatoes are cool enough to handle, rub off the skins. Squeeze out the tomato seed gel and either discard or use it to make tomato water.
Squish the peeled, seeded tomatoes into clean jars. Add acid to each jar, as above. Press hard to remove any air bubbles. Leave 1/2-inch head space in each jar.
Process pints for 30 minutes, quarts for 35 minutes.
Variation: Roasting the tomatoes instead of blanching them serves the same purpose of loosening the skins, but intensifies the flavor of the tomatoes.