Very often, in the process of recording a fragment, you'll remember more and more of the dream as you write. The important thing is to record whatever you do remember of your dreams as soon as possible. This method will put you back into the dream, and you'll find you remember more as you go along. You're not trying to write great literature, you're trying to record a memory before it fades. Over time, you'll probably find that some of the 'mistakes' are revealing.
Misspellings can reveal puns, and often dream items suffer from meaningful mistaken identities.
Especially important is anything that seems unusual or out of place. Imagine yourself back in the dream scenario. Be sure and record these impressions. After you've recorded your dream, date it, and then make a few quick notes on possible relevance to your waking life. These don't need to be complicated or particularly well thought out, they just need to be enough to jog your memory when you review the dream later on.