I and my father discuss our dreams with one another as we both have what we believe are prophetic dreams.
Think about the overall air of the dream, your attitude towards the events, your feelings in and around the dream and so on. Take that into account.
The symbolism of the dreams (the objects, people, animals, things, colours, places) are worth looking up, but Do Not rely too heavily on dream interpretation lists/sites/books/whatever. For example, cats, to me, signify myself and comfort, more than anything else. Cats are "good" in my dreams, even if in dream interpretation guides they are usually translated as "trouble".
And write down your dream when you wake up, in as much detail as possible.
And don't hesitate to talk about it with other people. Not so much because they can offer you some grand insight, but because by bouncing ideas off another person, or hearing the thoughts of another person, you can find your "own" insight, simply because your thought processes are running a little differently when you are discussing your dream with someone else than when you're just thinking about it yourself.
