I’ve been trying to lucid dream for about a month now, I’ve only done it 3 times and I can only remember about 1 minute of it. I usually remember at least 1 dream a night, but only in small parts. When the page says I have to remember at least one dream, does that mean I have to remember the whole dream? Is that why I can only remember parts of my lucid dreams, or did I fall back into a regular dream?
It sounds to me like you’re a natural lucid dreamer; you just need to work on your dream recall. Are you keeping a dream journal? Because that’s probably the best way to boost what you recall in the mornings. You might also want to try waking up at various points throughout the night and write down whatever you were dreaming. 
Yes, I do keep a dream journal. I only remember a bit but as I write I remember more and more. Still, I can’t remember the entire thing. Is that a prerequesite for having ‘good’ lucid dreams?
Not necessarily. I tend to remember my LDs a lot more clearly than my other dreams. But it definitley helps to be able to remember all of your dreams. It just takes practice. Keep at the journal and remind yourself that you want to remember your dreams when you wake up.
As long as u actually remember some parts of your dreams, its ok 
Yeah, a dream journal is the best way to make progress with dream recall abilities.
Man, all these 2-letter acronyms are so confusing…
You will get used to them…and remember, if u put your cursur over some of the acronyms, it will show u the name.
When I remember even a little moment of my dream I write it down on my dreamjournal.
Sometimes when I remember only a one image of some dream but I can´t figure any words to describe it, i make a note like: “I have a dream, but I can remember only one poor image of it”
Or something like that 
When I do that I can remember even that one image, because usually when i have wake up early(school or something) that one image is all I remember. 