I had this problem for probably the first year that I was here and it took several people telling me how before I actually figured out it was sitting right in front of my face. So, here is a more visible way of explaining it (don't mean to steal your thunder Pete, but I didn't finally figure it out until someone showed me a picture-lol).
So, what I'm sure you are doing is hitting "reply" and then hitting the "insert quote" button and then coping the quote in. That doesn't give you the information on top of the quote that you are looking for.
Instead, like Pete said, just hit the quote button on the post you want to quote from. So, if I wanted to quote from your post, this is what I would click
instead of clicking "reply."
That will bring you to a reply screen with the whole quoted post already in it. You can then delete what ever part of the quote you don't want so its not confusing.
I hope that helped.