If your main objective is some flavorful broth, you add whatever meat(s) you're using to a large pot of cold, well-salted water. Tonight, I used a lovely free-range chicken and a beef shank:

You bring the meats just to the boil, skimming off the scum that inevitably rises to the top as it comes to the boiling point:

While the water is coming to a boil, prep your aromatic vegetables. Immediately lower the heat to a very gentle simmer, skim off any residual scum and then add the vegetables to the pot:

Let the meat and vegetables simmer until the meat is quite tender and the broth has a rich flavor. The total simmering time depends on the meat being used: chicken will take an hour or two, depending on the type of chicken, while beef will take about three hours. If you're using both and plan to eat the boiled meats, then you may want to remove the chicken so it does not completely overcook. The water should totally cover all the ingredients, so add more if the water reduces too much, as it will tend to do. Test for seasoning, and don't be shy about adding generous amounts of salt. Broth should not be bland.

Once the meats are cooked and the broth has developed good flavor, switch off the heat and let the broth cool a bit. You can even let it rest on the stove (uncovered) overnight.

You can also use the broth immediately if you like, but it has a deeper, richer flavor after this 'rest'.

(Optional): If you want a clear broth --important when making a clear soup--strain the broth through the fine sieve or cheesecloth to remove the particles. (If you want a really clear broth, see note below.) If you wish to de-fat your broth, leave it in the fridge overnight; any fat will form a solid white layer on the top, which can then be easily removed.