I don't dream.
Of course you do. Everyone does. It's only that not everyone is able to remember their dreams. This is most often due to not getting enough sleep, or having sleep that is too frequently interrupted.
If you want to be able to remember your dreams, you'll first need to be sure you're getting enough sleep. Scientists have demonstrated that sleep cycle run in roughly 90-minute intervals, so six hours or 7.5 or 9 are ideal. Everyone is different, so find the amount that suits you, keeping in mind that if you've been sleep deprived you may have some catching up to do.
Also make sure (as much as you can) that you give yourself enough time to wake up. People who jump out of bed the minute their alarms go off seldom remember their dreams because their brains go right into whatever is facing them that day: work, kids, weekend activities. You're far more likely to remember your dreams if you wake slowly, loll in bed for a few minutes. That transition is important because you can stay partly within your dream and think about it, review it, before getting up and doing anything. And the more you do that, the more likely you are to recall all the little details that will fade as the day goes on.
If you're worried you won't remember it for long, do the old trick of keeping a pen and notebook by the bed so you can jot down the dream. Remember to give yourself enough time for this, too! Some may prefer to write the dream down like a story ("I was in a red room with black furniture, and I was nervous about something"), others may prefer to reduce it to a few key words or phrases ("red room, black furniture, nervous").
I've found that my previous night's dream often returns to me when I next lie down to sleep. This is because I've exercised and opened the lines of communication between my conscious and subconscious enough that, when it's my subconscious' turn to "speak," it picks up the "conversation" where it left off. That doesn't mean that my dreams are one continuous story, however; like any ongoing discussion, the topics change organically depending on what my mind finds most interesting or important. And just as in real conversations, when someone might suddenly say, "Oh! I just remembered!" my mind may jump from subject to subject as I sleep, the result being very jumbled dreams, or several different dreams over the course of a night.
And yet I also have days when I can't recall my dreams. These are often days when I've been awakened before I was ready, or sometimes when I'm dealing with unusual stressors and my conscious brain kicks on the minute I open my eyes, thus drowning out anything my subconscious might have had to say.
Dreaming takes practice, or really, remembering one's dreams does. Keep those lines of communication open as much as possible and get used to listening.