You just change the foot to a zigzag foot for the machine (probably a very standard screw-on foot that is widely available). Not sure what you mean about the feed dogs being for straight stitch? Maybe you mean the stitch plate is for straight stitching? Then you need to purchase the zigzag stitch plate for the machine.
Chances are good that the zigzag foot and zigzag stitch plate got separated from the machine a long time before the machine was dropped off at Goodwill.
Edit: Very clean-looking machine! The zigzag stitch selector is clearly visible in the photo. Also any machine that has different needle positions (this one has a center, left and right needle position selector) would have come standard with a zigzag stitch plate.