Hi Elisabeth --
I first started learning about my past lives by paying attention to things that intensely moved me for no apparent reason.
As Dave says, these lives come up in connection with some issue that is happening in your current life. For most of my life I've had to deal with the issue of slavery -- not that I was ever literally a slave, but I was raised to believe that my needs, preferences, and desires were completely unimportant, and that my function in life was to serve others and make them happy. Pretty good description of a slave. Anyway, I have always been extremely distressed by the knowledge of slavery and of institutionalized racial discrimination - not just like any normal person with a heart would be, but where my whole body would be possessed by outrage and a sense of injustice and anger when I heard about it. I started to understand that I myself had had slave past lives by doing things like noticing a scar on my ankle, and letting that kind of open my mind to the idea of a slave past life. I had an experience where I allowed myself to emotionally go into the state of one of these lives, and I learned the name of this person and everything about his life (American South, his name was Thomas Payne). I did this by myself, without anyone else there.
I also believe I was a slave in Ancient Greece, because when I learned about the philosophy of Aristotle in class for the first time, I was overwhelmingly flooded with sensations of him as a person, of knowing and loving him as a person, things having absolutely nothing to do with the actual philosophy and completely not present in reading about his philosophy (or really anything about him, I've come to find out). I then had a dream-experience that wasn't really a dream - it was like I was in some in-between state between dreaming and awake. Everything was absolutely black, and in that blackness I knew everything about Aristotle and his philosophy. I understood it perfectly. As soon as I woke up, it was all gone. But since then I have looked into the life of Aristotle and it turns out he did teach and have intimate relationships with some of his slaves. I had strong images of walking through gardens and talking with him, and I also found out later that that was how he usually taught his students.
I've also had some intense past life memory experiences with my ET when we first were getting to know each other. I don't know how to explain it other than we went into a kind of trance state, without trying, and in one of these states we re-enacted a life where he was the slave woman and I was the young girl of the house (American South). In that life, she was more of a mother to me than my real mother was. In another we were brother and sister in Ancient Egypt and we were intensely in love with and sexually attracted to each other.
I haven't had any experiences like this in a long time, or maybe if they happen they are just a lot more subtle now.
Anyway, the way to do it is to pay attention to little things that pull at you for no reason you can explain. Open yourself and go into them, and see where they lead you