Wash the tomatoes. Choose blemish-free ones and cut away the stem end.
There is no need to peel, but remove as many of the seeds as possible. Paste tomatoes can be squeezed to remove most of the seeds. It's ok if there are still a few left behind.
Place the tomatoes in a large stock pot that can handle cooking acidic foods. Cook the tomatoes over medium heat (or whatever is needed to maintain a low boil). This part of the process will take several hours. Stir the tomatoes every 20 minutes or so to prevent them from sticking and burning on the bottom of the pan. Reduce the amount of liquid by about half. The amount of time this takes will depend on the types of tomatoes you used, their moisture content, and how hot you are cooking them at. Expect it to take several hours. Allow the tomatoes to cool.
Blend up the tomatoes into a smooth sauce using a high-powered blender, food processor, or an immersion blender until nice and creamy. Spread the blended tomatoes into a baking pan. Keep it to one inch thick or less.
Bake the tomatoes at 250º Fahrenheit for an hour. After an hour, give the tomatoes a good stir. The paste will still be fairly runny at this point.
Cook the paste for another hour and repeat the process until you get a thick consistency. Stir every half hour to prevent burning. This can take 3 to 4 hours or longer, depending on the moisture content and thickness of the tomatoes.
Allow the tomato paste to cool completely. Store in quantities you prefer. I like to use either a cookie scoop or silicone freezer molds. Flash freeze the paste. Once they are solid, remove them and store in freezer-safe Ziploc containers or bags. Pull and use what you need for your recipes; no need to thaw for cooked dishes.