Hi Nancy,
If it is like my 185J, there is a big wing-nut on the bottom of the base. You just unscrew that and the base should come off. Be careful, the plastic on these is about 50 years old now. Hopefully your base is still in good shape and has all the supporting fins intact. The serial number is stamped into the underside of the machine, I think on the end near the slide-plate, can't remember for sure.
Happy sewing!
Pat