A good place to start is to review the dream in your mind from beginning to end as you're waking up, before you open your eyes. This will help you to remember it better.
Then - write your dreams down as soon as you wake up, when the details are still fresh. There is a lot more information being given to you during this time than at other times of the day. If you don't write down your dream, you're likely to forget it.
Think about what in the dream stands out or seems most important, such as items, symbols, people or events.
Consider what happens in the dream, but also how it happens. Not just who's in the dream, but where they are and what they're doing, and what stands out about them.
Pay attention to what your intuition says about why you had the dream.
Also, never be afraid of your dream. A scary dream/nightmare does not mean that something bad is going to happen, but usually just that you need to slow down and take a break, think of where you are and be true to yourself and your needs. After all, you created the dream, and so on some level you already know what it means.
I also found this really good article by Annie Wright which can be helpful.