Understanding and memorising is the best way.
However, you can just work it out on the fly using logic and the data
For example:
PED, -20% change in price but only +10% D means inelastic as D less than responsive to change in price. calculate it and sure enough its less than 1 (0.5)
PES, same as above but with S
YED, income raises and demand falls? inferior. Income raises and so does demand? normal or luxury(more elastic).
XED, price falls for one product and demand for the other rises, compliments(visa-versa for substitutes)