When you wake up from a dream, try not to do so as a result of an alarm clock because that'll draw your attention away from the dream which'll make it easy to forget. If you over-concentrate and try to decipher the dream, you'll just end up making up pieces and confuse yourself, just jott down the smallest things you can remember, no matter how irrelevant they may seem. And carry a little notebook with you throughout the day in case you remember something. Oh and before you go to sleep, place a note in the first place you'll look, when you awake, that says "what did you dream?". It's also very important that you aren't sleep deprived as that will make you very groggy and tired when you first wake up, which'll make it more difficult to recall your dreams. The more you attemt this, the easier it'll be to recall your dreams.
I wish you the best of luck and I hope that you can remember your dreams real soon .