What's the key to making thick soups? I looove soups, but I mainly eat vegetables and I do not use any store-bought spice mixes or "stocks". I also do not eat dairy for other reasons. And I also do not fry things.

I remember my grandma making nice, thick soups, ones that are not so watery... But I really don't know how to make them! My soups are either watery or they're overcooked.

So what is the key to making a soup that is thick and isn't overcooked? Or is there no key, it just depends? If that is so, then I want to know what it depends on. :-)
Make your favorite vegetable soup.  Remove 1/4 and puree in blender.  Return to the rest of the soup.  If it is not yet think enough, increase the amount you remove and puree until you find the consistency you are looking for.  If you don't have a blender, you can use an immersion "stick" blender, or even a hand cranked food mill. Alternately, if you have none of these devices, simply put the veg. in a bowl and mash with a potato masher.