If you attempt to try and block your ears when flying, you are most likely to end up with a perforated eardrum for your troubles. Swallowing, yawning, or holding your nose and blowing through it gently are the best methods to equalise the pressure difference you are experiencing. If you are unable to clear your ears, you should not fly. Similarly, if you are having sinus problems. Trapped air in various body cavities will expand as you climb, and even very small amounts of expansion can be extraordinarily painful. Anybody who has suggested to you that you should actually try and make this happen artificially is a total fool.
It also does not happen suddenly on take off or landing, it probably just seems that way. Air pressure changes fairly gradually as you climb and descend, with the rate of change carefully controlled by the aircraft pressurisation system to avoid any large or sudden changes. Your body however does not always compensate for these pressure changes as smoothly as the aircraft, and so you get regular small and sudden equalisations of pressure, which are the 'pops' you experience in your ears. Air will try to exit your ears on the way up, and enter on the way down, and I suspect it is the physical make up of your inner ear that makes the latter more noticeable.