"I sincerely want to improve my Avodat Hashem by mastering my eyes. Where do I start?"
AvodatHashem - Divine Service - is a general term that embraces a wide range and many levels of Torah observance. For our purposes, we are defining "Divine Service" as compliance with Torah Law (Halachah) and Torah Ethics (Mussar). In this light, Divine Service encompasses the fulfillment of the mitzvot (the positive commandments), and the avoidance of aveirot (the prohibitions).
Simply put, an observant Jew performs Divine Service by observing the Torah to the best of his or her ability.
A person's real essence is his soul, which by definition is holy. The soul is entirely spiritual, but because it is attached to a physical body, its spiritual light becomes dimmed. The expression of that spirituality is through a person's good character traits and mitzvot. A tzaddik is often described as having a "shining countenance" because his soul is so developed that he is radiant. If we neglect our spiritual side, however, bodily forces gain the upper hand and base character traits, followed by aveirot, emerge.
"My son, give Me your heart and let your eyes observe My ways." (Mishlei 23:26) The Midrash explains that Hashem is saying, "If you give Me your heart and eyes, then you are My children." This means that control of your heart and eyes is a major criterion for being close to Hashem.
Viewing improper images creates a detrimental force which can easily overturn our spiritual equilibrium. It has the power to undo our entire spiritual foundation. How is that?
Your soul is a fiery element. Just as water extinguishes a blazing fire, the tumah of these images extinguishes our spiritual powers. Even worse, since the eyes are connected to the brain, the images that we see remain lodged within our mind, causing lingering ill effects.
Just as actual vision is impaired when the physical eye is injured, spiritual vision is impaired when the eyes are exposed to immodesty. This damage diminishes our ability to perceive the truth and to connect to Hashem.