Think of a diaper change like a puzzle, make sure to have all the essential pieces (diaper, wipes, some place to dispose the diaper), give yourself enough room to work on it comfortably but get comfortable with a small space (at least the size of a handicap stall as that's what you'll be working with, optimally get comfortable changing in half that size in case a handicap stall isn't available)
Then you need practice ,
first take the diaper out of what you have it in, stretch it out and fold it down the middle to create a valley between your legs so the urine will naturally travel towards the center of the diaper,
then slowly slide down your current diaper, make sure you currently aren't in process of going before you completely slide down, when you are sure remove the old diaper set it to the side immediately wipe up the current area getting it as clean as possible,
then after that put the new diaper under you try to get it anchored, if in a bathroom stall I advise using the one of the walls of the stall then I advise starting with the bottom tapes making sure they are sorting of pointing diagonally upwards, make sure it is snug at the leg gatherers, this is the difference between wet pants and a soaked diaper later,
then do the top tapes pointing downwards making sure there is a barrier at the waste, failing to do this can also lead to wet pants to a wet shirt,
when you are sure you are finished check to make sure there is no exposed pots around the diaper that will leak when you move, make adjustments if need be to fix this, then wrap up the old diaper pull up your pants making sure your diaper is covered,
then go and throw away the old diaper wrapped up in an appropriate trash receptacle