When you know, you just know. It's a gut feeling. It goes beyond just having a fascination with a certain time or place, although this can be a big clue. But it is just as likely that you may have a feeling of revulsion or disinterest for something that recalls another life. There are many experiences on planet earth that, having lived through it once, no one in their right mind would want to revisit. So nostalgia is not the only indicator, but it is a good one.
Memories of other lives can surface in a lot of different ways. They can come in dreams, or while you are awake. They can come up when you are daydreaming or fantasizing. A past life memory can feel like something you just made up off the top of your head, or it can feel like a full-blown hallucination. I would bet that most of the time people just dismiss glimpses of other lifetimes because the information seems too disjointed and nonsensical. Memories can be very slippery, and tricky to interpret, but once you remember something clearly, it can never be taken away from you.
I have known people who were able to regress themselves and recall an entire life in one go, and I would love to be able to do this. I saw an entire past life in a dream once. I witnessed every moment of it from birth until death, and at the end I was told that this person was me. I was too blown away to hold onto any details, and in the end those don't matter much anyway. What matters most is the feelings you had, and the people you loved.
One of the most powerful things that can happen is you meet other people you have known in your past lives, and you start talking and remembering things together. This can happen with people you meet in physical reality, or in non-physical reality. Love opens doors to memory as nothing else can. I have had dreams where I was talking with soulmates about being together in future lives too.
In my experience understanding past lives is like putting together pieces of a puzzle without knowing what the final picture is supposed to be. Some memories don't make sense until other things fall into place. You are oriented at a particular point in time and space for a reason. If you get too much information coming in from other coordinates, it can really throw you off balance. That's why clear, unobstructed past life recall is rare. Do not have a horrifying past life flashback while driving a car or operating heavy machinery.