Chop onion, tomato and carrot. You don't have to cut them up too small because in the end you will use a blender.
Sauté onions in olive oil or cooking spray until transparent.
Add carrots, sauté for a minute or so, add tomatoes, sauté for a couple of minutes more.
Add water. Boil. Add a little salt, or you can skip the salt. Add cayenne pepper or red pepper flakes (optional).
When the carrots are soft (boil about 15-20 minutes), pour everything in a blender. Blend until smooth.
Pour contents back into the pot, if the soup is too thick you can add some more water, but it shouldn't be too watery either. Boil for a another minute.
Serve with or without a dash of fresh lemon juice.