Scoop the onion into a small strainer and rinse under cold water. Shake off the excess water and transfer to a large bowl, along with the green chiles and tomatoes.
Cut around each avocado, from stem to blossom end and back again, then twist the two halves apart. Scoop out the pit and discard. Scoop the flesh from the skin and add to the bowl. Using an old fashioned potato masher or a large fork or spoon, mash the avocados into a coarse puree, mixing in all the flavorings. Taste and season with salt and lime juice - the guacamole usually takes about 1 teaspoon of salt, lime juice is a matter of personal preference.
Cover with plastic wrap directly on the surface of the guacamole and refrigerate until you're ready to serve. Scoop the guacamole into a serving dish, sprinkle with a little chopped cilantro and queso fresco (if you're using it) and you're ready to serve.