I don't feel there is a definitive way without training but most women have a feeling imho... I have delivered six kids and been pregnant ten times... I knew about where they were in all but one of my six babies and the sixth it may have been because we lost her before she got bigger...
In the ones where my sons were felt much later the placenta was in the front felt earlier the placenta was in the back, in ones where I had lots of spotting or spotted after intercourse I had a low lying placenta including placenta previa... So while it's not an exact science it can give you tips to just help you pinpoint it.
Welcome to Mothering! We look forward to reading your posts.
In addition to joining in discussions around the community I suggest you also join your Due Date Club here at Mothering so you can get to know the other Mothering moms who are due the same month as you. They offer you support and share their experiences through their pregnancy and birth. Also, we throw a baby shower for each due date club. Lots of fun! You'll find them here: http://www.mothering.com/community/groups/