Salsa means sauce, but there are a great variety of salas to be had.
It sounds like you would like a fairly chunky tomato salsa.
There are many approaches to this, and an infinite variety of recipes. There is no single answer to how you would prepare your tomatoes.
Choose your preparation method based on the the outcome you like. Many tomato salsas are uncooked, so you would simply use raw tomatoes. You can also roast your tomatoes to intensify the flavor, or even put some dried tomatoes in with your salsa—there are no rules.
Some common options:
Use diced or whole canned tomatoes, further chopping them to your desired size. In the winter or when good tomatoes are not available, this is a good option.
Dice fresh tomatoes (and other vegetables) to the consistency that you desire.
You can also pulse some (or all) of your tomatoes, either fresh or canned, in a food processor, to get the consistency you desire.
You can also combine these methods, for example by pureeing part of the salsa for the body, and adding diced or chopped tomatoes and other vegetables in for texture.
Some salsas are cooked in which case you might only rough chop the tomatoes before simmering, and let them cooked down to the consistency you like.
Since you specifically mentioned jarred salsas as your model, I imagine that you may desire a lightly cooked salsa modeled after typical Mexican restaurant salsa. One easy way to do this is to start with canned tomatoes which are already cooked:
- Whole canned plum tomatoes (or diced if you don't have whole)—depending on your taste, you may want to drain the excess liquid from the tomatoes
- Diced onions and or garlic
- Chopped fresh, roasted or canned chili peppers (roasted pablano are especially good here, or perhaps a jalapeno or Serrano)
- Other seasonings to taste, such as dried chili powder (I like ancho), cumin, maybe some Mexican oregano, perhaps a pinch of cayenne. Cilantro is evil, but put it in if you must.
- Salt to taste
Place it all into the bowl of a food processor, and pulse until it is chopped to your desired consistency. If you let this sit for an hour or two in refrigerator, the flavors will blend and mature.
Pioneer Woman has a very similar recipe, in detail, with a great number of photographs. Note that you do not have to pulse yours as finely as she shows.
Note also that restaurants also often serve pico de gallo, which is essentially just chopped tomatoes and onions, perhaps with some chili peppers and other accents (probably including evil cilantro) that have been allowed to sit together a bit to marry. It has almost no sauce like body, but is more like a chopped salad. This is typically made from chopped, squeezed, fresh tomatoes.