Number One
Pay more attention other than your self.
This is super important in observation because you're trying to observe the world and not yourself. So many people spend the days wondering what others think of them if they will mess up in a conversation or how they look if you're actually trying to increase your observational skills spend your energy and focus on others not just yourself.
Number Two
Notice changes.
When you start observing you can easily notice things out of place so you should get a reference point. First set a baseline for everything. How many times did that woman blink before you started talking about foreign affairs, What was that guy doing before He crossed his arms, What has he been doing it all night. Changes what is important not just how someone act.
Number Three
Put away distractions.
To become a better observer you must put away distractions. How can you notice subtle changes in body language or the size of someone's pupils if your phone has all your attention. There's all kinds of distractions in this noisy world but if we can laser focus on something we are observing you'll increase your chances of understanding the situation better.