To remember your dreams, you should wake up around the end of a REM sleep phase. Since dreams (the most vivid ones) happen during this phase, when the activity of your brain peaks during the night, waking up right after it maximizes the likelihood of retaining the dreams just experienced.
Try not to get any distractions, and note down the details of your dreams as soon as you open your eyes to avoid covering the memories with the day's events. Read more