How can someone most easily relieve depression without taking any pills or medication?

Psychotherapy. You can treat depression effectively by psychotherapy alone, but it requires a therapist with experience in treating depression. Generally insight-oriented psychotherapy works much better in the long term than does cognitive-behavioral.
Lifestyle. Mild to moderate depression can be treated by improving your lifestyle: add omega 3 dha (better for the brain), vitamin bs and more b12, vitamin d (your happy hormone), sam-e, exercise, low glycemic foods so you dont have sugar swings worsening your depression and reducing the caffeine/alcohol. Psychotherapy, acupuncture, cognitve behavioral therapy can help as well.