Carol
Just so we have our terminology straight, let me identify some parts of the door so we are all talking about the same thing. Excuse me if you already know this stuff. The panel is the center of the door. The vertical side pieces are called stiles. The horizontal top and bottom pieces are called rails.

The panel fits into the stiles and rails usually about a 1/4". To quiet the rattle, pin the top and bottom of the panel in the center edge of the rails from the back side of the doors. All this work is from the back side of the doors. Several ways to pin it. A well equipped shop would use a pin nailer. If you have an air compressor you might get one at Harbor Freight, but it is a tool not often used even by the most ardent woodworker.

Another approach would be to get some brass #4 screws about 5/8" long and drill a pilot hole into the rail about 3/16" in from the panel. Drill a little ways into the panel. Then carefully drive the screw straight in. If they are real brass screws, drive a real steel screw in first. Back it out and replace with the brass screw. Brass is too soft to make its own path well. I would use a flathead screw with a Phillips head drive. Slotted screws are a disaster in the making in my shop. You will have to slightly countersink the hole. Simply use a countersink bit. A small single flute will work the cleanest. You can get this at real tool store. This would leave a tidy repair you should be able to live with.

Another approach would be to find the nearest woodworking club in your area and go make some friends to show you the ropes. If there is a Rockler or Woodcraft store, you will have a place to start. Also tell us where you are and maybe we can direct you better.

Hope that helps some.