There is a standard protocol you can use to talk to a GPS module. I forget what it is, search the Web. Any microcontroller can interface with it. PIC seems to be the most common controller for hobbyist use. There are GPS modules on eBay which don't have a screen or maps, they just output coordinates.
GPS cannot determine which direction the machine is pointed in. As such, if you have no data on its direction, all you can do is drive forward and see what direction it moves the coordinates in. Lack of high resolution accuracy in GPS may require a fairly long drive to figure this out. Fortunately, while GPS has at best around 30 ft absolute accuracy, the relative accuracy to a measurement taken minutes ago can be quite accurate with a precision receiver. A magnetic compass may help determine direction much quicker.
Once you know the machine's orientation, you'd just steer towards in and hope there's nothing in the way. Many microcontrollers have plenty of room for whatever nagivation program you care to write.