It is absolutely possible to FMQ on an "regular" sewing machine. All you need is a machine that does a straight stitch, a way to either drop or cover the feed dogs, and a FMQ foot (a.k.a. a darning foot on most machines), and a foot control. The machine I do my quilting with doesn't have any fancy stitches.
I'd recommend you do a lot of practicing be for diving into trying to FMQ on an actual quilt though. There is a lot of information on this site about how to get started. You'll also find some great resources on youtube and my favorite is Leah Day's site at
http://freemotionquilting.blogspot.com/