Most people dream every night, yet recall only fragments. Sleep researchers generally find that recall is highest on waking straight from a dream, and that the memory fades quickly once you get up and start the day.
The habit that helps most is also the simplest: keep something to write with within reach, and record before you move. Lie still, let the last scene come back, and write whatever is there, including feelings and half-images. Do not wait for it to make sense.
Some people find it helps to tell themselves before sleep that they will remember. It is not a guarantee, but it points attention at the task. An irregular schedule and late alcohol are often reported as making recall worse, so a steady routine is worth trying.
Write the date, then the dream in the order it came, then any feelings on waking. Short is fine. A single line such as "teeth, my old school, embarrassed" is enough to keep the thread. The dream journal on this site highlights dictionary words as you type, which can jog the rest of the memory.
If you recall nothing for a week, that is normal. Keep writing "no dream remembered" and notice how often a scrap returns. For more on how researchers study dream recall, see the DreamBank at UC Santa Cruz and the overview of dreaming on Wikipedia.
This guide is general information, not medical advice. If dreams or sleep are affecting your health, speak to a doctor.