Chicken soup is a prototypical comfort food. For many people it's good example of home cooked food. The smell of chicken soup evokes a sense of home and being nurtured.
The basic ingredient is chicken broth. The broth can be bought or made.
Other common ingredients are pieces of chicken, vegetables (carrots, potatoes, celery, mushrooms, onion, leeks, corn), and carbohydrates in the form of pasta, matzo balls or dumplings. Then there are the spices: salt, pepper, bay leaves, ginger.
For a homemade broth, cut most of the chicken off the bones of a cooked chicken, then put the bones in a pot, cover in water and simmer for at least an hour. Some people think you get more flavor if you break the bones up. Strain the bones and chicken bits from the juice or broth.
Chop the vegetables to bite sized pieces. Cut up pieces of chicken. Add to the broth. Season with the spices you like. (No spices are required, but salt and pepper are common.) Continue to simmer until everything is cooked. Chicken pieces should be cooked through for safety. Cooking too long after it's done can make the chicken stringy or rubbery. Vegetables should be cooked to your preference, usually until soft. The amount of time required will vary based on the size of the pieces, the temperature and whether they were pre-cooked.
See references below for links to even more recipes.