These two words are not synonymous. Continuous means an unbroken event or series of events. Continual means events that occur repeatedly but not in an unbroken period of time:
The snow fell continuously from Monday through Thursday, leaving four feet of snow over much of New England. (It never stopped snowing.)
The snow fell continually from Monday through Thursday, leaving three feet of snow over much of New England. (It snowed on and off during those four days.)
I wish I had a simple way for you to remember the difference between these two words. The only idea I can come up with is that continual is a shorter word than continuous; the snow that falls continually has breaks, so it falls for a shorter period of time. Any better suggestions will be greatly appreciated.