I've had conversations with a lot of people who have told me that they dream all the time, but can never remember their dreams for more than a few minutes after they wake up. Personally, I've made mental notes to tell a friend about a particularly interesting dream, only to find that the details and sometimes even the entire plot of the dream have completely slipped from my memory.
It's easy to assume that the ability to remember your dreams is pre-programmed like your hair color or shoe size, but there are actually plenty of ways to train your brain to hold onto those dreams long after you wake up.
Get more sleep.
It may seem like common sense, but a good night's sleep makes it easier to think clearly in the morning. Going to bed a bit earlier and waking up with a sharp mind can help you to process your dreams and recall more details.
When you wake up, try to stay in the same physical position while you think through last night's dreams. The sensations of moving around and stretching signal the brain that it's time to transition into the waking world, making it harder to keep the details of your dreams in mind. Keeping still and consciously reviewing the contents of your dreams each morning will train your brain not to throw away those memories when you get out of bed.
Write it down.
Dream journaling is a valuable habit to form. Keep a notebook and pen next to your bed, and after reviewing your dreams in your head, write them down in as much detail as you can recall. This will help force your mind to reach back and fight for those memories that you might otherwise lose.
Practice & Prepare
Each night before bed, read through your dream journal from the previous morning. Run through your last dream or two, and then repeat a mantra of affirmation to yourself right before going to sleep. Telling yourself "I will remember tonight's dream" or "I will dream vividly" is a simple way of reinforcing the habit and adding intentionality to desire.
The brain is a flexible thing, and just as it can be trained to be better at math or speaking German, it can be trained to remember dreams with more clarity and detail for longer periods of time. The more time you spend connecting with your dream world, the easier it will be to have more vivid and advanced lucid dreaming experiences.