First, you should get lots of sleep to remember your dreams. That way you'll be more focused to achieve your goal of recalling dreams. Besides, dream periods get longer and closer together as the night proceeds. The first dream is the shortest, perhaps 10 minutes in length, while after 8 hours of sleep, it can be from 45 minutes to an hour long.
It's useful to keep track of your dreams by writing them down in a dream journal. Keep it handy by your bed and record every dream you remember, no matter how fragmentary. Write everything, even if all you remember is a face or a room.
You'll need to write in your dream journal as soon as you wake up, because during the day you may find you remember nothing about the dream. It seems like we have a built-in dream eraser in our mind. If you don't feel like writing out a long dream story at 3AM, note down key points of the plot. Also write down the precise content of any dialog from the dream, because words will almost inevitably be forgotten in a very short time.
I'll upload part 2 in a while after I finish it :)