The key to improving your ability to read greens is first to recognize that effective green reading involves skills that can be developed. Reading greens is not a mystical art form. Instead, green reading is based on the structured principles of understanding Slope & Friction.
Understanding slope involves first recognizing how to see/find it and then learning to judge the direction of the slope. This can be done by using one’s feet, eyes, and knowledge of greens via greens books and playing experience. Second, is the skill of judging break amount. While this is more complex, it involves factoring in slope direction, slope amount, your putt’s relation to the slope, and friction of the green- what we refer to as “stimp” in the golf world. factoring these together helps a player decide where to aim and how much break to play.
Therefore, to read greens effectively, the goal is to first get good at recognizing and judging slope direction and then estimating the amount of break to be played on a putt. I recommend most amateurs find a qualified teacher in their area who has experience in the principles of green reading or who can instructor them on a reputable green reading system. Green reading is probably the most critical skill in putting, and learning to improve this area of your game can provide great dividends, whether playing on the weekends for fun or in competition.