Usually, I'll remember as something is happening that I had dreamed it before. The problem is knowing before it happens that it was a premonition instead of just a regular dream. Try a dream journal for a while and see what comes of it.
Most times, these are small things like a conversation (deja vu) or running into someone you haven't seen in a while. My biggest one was dreaming my wedding a week before I met my husband. It didn't seem like a big deal when I woke up, but when I was introduced to him later, I was completely floored!