There are a lot of different methods people have used to better remember their dreams. Among them are setting intent and journaling. Slight alterations to sleep patterns may also be effective.
Setting intent can be done in a spell. Some make a sigil (a basic statement of either can be, 'I remember my dreams'), and some just use a mantra. Many people have reported success. With a mantra, basically the statement of intent, whether the one I listed or any other which is used, is repeated upon lying down to sleep.
Journaling is an interesting practice, which takes dedication. it may not seem to work so well at first, but it can have long-term and lasting success. It is simple: Keep a notebook of some sort, and upon waking, even if in the middle of the night, jot down whatever dream(s) you remember. List the date and time of waking. Some people may also incorporate this with a sleep habits journal, to gauge if a different bed time may help their quality of sleep and ability to remember dreams. If no dream is remembered, that should be recorded -- not so much as you did not dream (as we all dream, even when it is not remembered), but that the dreams were not remembered. Basically, it embeds a subconscious idea that dreams are important, and should be remembered.
Modification of sleep schedule can lead to sleep deprivation, and make you tired, so beware. But here is how and why it may help remember a dream upon waking (it is what most of the rest of this post will focus on):
The time of dreaming is on the way to the deepest stages of sleep, and after the deepest stages of sleep. That is, it's a deep-ish state, but not the deepest, and not when your brain actually rests. In reality, the brain can be more active during dreaming than waking hours. Any way, dreams are likely to occur shortly after slipping into sleep, and shortly before waking up.
You are least likely to remember dreams which you have before the deepest part of your sleep, unless something wakes you up, such as a loud noise or a hypnic jerk. So it is best to focus on the dreams closer to waking up.
One method is closely related to some advice on having a lucid dream: Setting an alarm a little earlier than the final alarm for the morning. Twenty minutes is minimal, though some people choose an hour or two. Yes: This snaps you out of a deep sleep, whether in the deepest state or REM (rapid eye movement, the stage of sleep when dreams happen) sleep. But turn off the alarm, and go back to bed. It should be a gentle enough alarm not to make your heart race, and close enough that you don't have to move a lot to turn it off; the goal is to wake up then return to sleep. More likely than not, if you were not disturbed too much, you will go quickly back into a sleep state, deep enough to dream. Its brevity will prevent the very deep state of sleep, and dreams should be remembered from this period more easily.
Some more notes on dreams:
You will best remember your dreams immediately when you wake up. Most people forget as much as 90% of their most recent dream an hour after waking. After that point, everything is remembered vaguely at best, and is an indefinite blur. The exceptions are very vivid and unusual dreams.
People forget the vast majority of dreams. As mentioned above, dreams experienced before the deepest portions of dreams are almost always forgotten. The earliest dreams when entering REM sleep afterwards are also mostly forgotten. Most people really only remember dreams which occurred immediately before waking.
This is a strange phenomena I have experienced throughout my life. I can list the number of dreams I remember per year and even in my entire life on one hand. I toyed with the idea of a dream journal but upon waking I never recalled any facts to write down. It's strange because we know all humans dream yet for some it feels as if we don't dream at all. There are positives though. While I personally never recalled good dreams I never recalled bad dreams either. The rare dreams I did remember were mundane and boring. I'm 27 and a few months ago I had my first nightmare or rather the first one I ever remembered:). I did some research and while I didn't feel like a deep sleeper everything I read indicated that those who slept deeply tend to not remember their dreams. Anyway to stop droning on the tips mentioned above sound promising for you. Any goal is achievable but there is always a silver lining.