Wash the tomatoes. I used about 3-1/2 pounds of San Marzanos (with a few Black Plums thrown in). You can use any kind of tomatoes you want. Or you can use odds & ends of tomatoes that you've saved in the freezer. (You are saving your tomato trimmings, aren't you?)
Dice the tomatoes or cut them into quarters. Whatever. Throw them in a big pot. (Or put them in a slow cooker. Or put them in a baking pan for oven roasting. Whatever. You decide how to cook 'em.)
Simmer on the stove (or roast in the oven, or cook in the slow cooker), stirring occasionally, until the tomatoes are good and fallen apart.
Smoosh the cooked tomato goop through a food mill. If you want really smooth paste, use cheesecloth or a jelly bag with your food mill. I don't bother anymore--it's messy, and I don't mind the little bits of pulp left. You can also whiz the tomato goop in the blender and then smoosh through a colander or strainer. Whatever works for you. Make sure you scrape all the good stuff from the outside of the food mill/strainer/colander. Don't waste anything.
My 3-1/2 pounds of tomatoes yielded about 3 cups of sauce and just a wee bowl of seeds and tomato skins bound for the composter. That's 'cause I smoosh the daylights out of my cooked tomatoes so I don't waste anything.
Return the tomato sauce to the stove/oven/crockpot and cook to desired consistency (sauce or paste). Don't forget to stir every now and then. Enjoying myself on the deck, sipping a Bloody Mary and shelling dried cannellini beans, I completely forgot about my paste toward the end of cooking, so it's a bit thicker than I wanted. But--WOW--is it yummy.
Store your paste. Each of these ice cube compartments is one tablespoon. I'll pop the frozen paste cubes into a big Mason jar and freeze until needed. Sometimes I freeze paste in 4 oz. jelly jars, which is a handy size. I usually freeze sauce in pint and half-pint jars.
You can make juice or sauce the same way, just don't cook it as long (obviously). If making juice, you'll want to strain the tomatoes earlier than I did, just when the tomatoes start to give up their juice, or you'll have sauce instead of juice.
Some folks add herbs, garlic, onion, olive oil, etc. when they make paste (or sauce). I don't. I want just tomato. I'll add seasoning when I cook whatever dish I'm making.