Here’s some great links on the topic:
The memory of our dreams elude us the moment we wake up. Our mind usually discards the experience, as we have, throughout our life, ignored most (if not all, depending on who you ask) of our dreams. So, it’s obvious we must train the mind to “see” our dreams as something worthy of remembering. We do this in a number of ways, examples include: reading about lucid dreaming or dreaming in general, keeping a dream journal, rereading past dream journal entries, etc.
What you’re doing right now is sufficient. There is of course, much more you can do to improve. What’s recommended is remaining still as soon as you wake up (don’t turn around or get up, I know, it’s easier said than done, but only in the beginning). Stay a couple of minutes there, just thinking about the dream you just had. If nothing comes to mind, think about your current emotions, write the first thing that comes to mind. If you’re still stuck with nothing, then write exactly that in your dream journal entry. Your purpose right now is to create a feeling of expectation. You want your mind to believe that you’re expecting to write something (your dreams) the moment you wake up. With practice (and patience) you’ll soon find it easier for yourself to remember more and more details about your dream(s).
Another tip, one that works wonders, is to simply repeat an affirmation before you sleep. A simple 4 or 5 times is enough. I personally use, “I remember each and every single one of my dreams for the night.” I repeat this as I lie in bed, and next thing I know, I’m finding myself awake multiple times throughout the night, with as much as 4-5 dreams by morning to record!
A final tip, one which often gets overlooked, sleep healthy.