My mom went out and bought a super old dryer to replace one that busted. I'm trying to hook it up with 4 prong cord hut there is no green nut for the ground. Where does the ground go?
A modern dryer should have a separate ground (which is bonded to the exposed metal case of the dryer) and neutral connection, with a removable jumper between them.
Unfortunately, I can't seem to find an installation manual for this model, just several copies of the Use & Care Manual. There are three possibilities:
The dryer has connections for 2 hots + neutral and no wiring at all for ground and the metal parts of the dryer are not connected to the neutral. You can test this with a multimeter by seeing if there is continuity between unpainted metal parts and the neutral connection. If there is no continuity (and you really truly have no ground connection on the dryer anywhere) then "a self tapping screw and secure the ground in the connection area be sure not to poke any other wires" is the right answer as it will provide a reasonable ground connection independent of the neutral connection.
The dryer has ground & neutral bonded together with a jumper. For any dryer made after 1996 (and possibly even a little older) there should be a jumper and by removing the jumper have ground independent of neutral. If you test with a multimeter and find continuity between the metal parts and neutral then if you can find and remove this neutral-ground jumper you can then connect ground to the case with a self-tapping screw and be safe.
The dryer has ground & neutral bonded together but no specific connection can be found. If this is the case then you have a 3-wire connection forced on you. If you were to connect a grounding wire to the metal case, you would effectively be bonding neutral & ground so that even though you are using a 4-wire connection, safety-wise it would be exactly the same - with the same dangers - as a 3-wire connection. If this turns out to be the case then I do NOT recommend this as (a) you are cheating well-established (> 20 years) safety standards and (b) likely have a VERY old dryer.
Bottom line: If you still can't find a jumper, check for continuity between case and neutral. If you don't have any continuity (check multiple locations to be sure) then ground to the case. If you do have continuity, get a different dryer. Used is OK, as long it isn't too old. Anything newer than 1996 should have a removable jumper so that you can connect it correctly.