I've found that a good way to help remember more of your dreams is to remember what you can then start asking more specific questions about the scenes you remember.
For example: I dreamt I was going to a foreign country with my father, like we did earlier this year. However, my boarding pass apparently was incorrect. My boarding pass was going to Hong Kong and the name on it was wrong. SO I asked myself "Where was I supposed to go in the first place, and what was the name on the incorrect boarding pass?"
I later wandered across the airport, looking for the entrance to the ticket counter, passing a few fast food stands. "What were they serving there?"
