If a dryer has a green ground wire that was connected to the green wire on the 4 prong cord what do you do with the green wire now that you have a 3 prong cord?

In a nutshell, you need to connect your green grounding wire to the white grounded conductor (that originates in your existing 3-wire dryer receptacle that does not have a green grounding conductor).

My answer assumes that you are in the United States. If not, the information below may not apply. In 1996, the U.S. National Electrical Code implemented a new rule that no longer allowed the grounded circuit conductor (white neutral wire) to serve as the grounding conductor (green wire) for many household appliances. New installations of ranges and clothes dryers must have a separate green or bare grounding conductor.

Now, there is an exception for existing installations. I have put BOLD emphasis on parts that may apply to your question. The text in brackets [ ] is not part of the NEC but explanations added by me.

NEC Article 250.140 Exception: For existing branch circuit installations only where an equipment grounding conductor [green wire] is not present in the outlet or junction box, the frames of electric ranges, wall-mounted ovens, counter-mounted cooking units, clothes dryers, and outlet or junction boxes that are part of the circuit for these appliances shall be permittedto be connected to the grounded circuit conductor [white neutral wire] if all the following conditions are met.

(1) The supply circuit is 120/240-volt single-phase, 3-wire; or 208Y/120-volt derived from a 3-phase, 4-wire, wye-connected system.

(2) The grounded conductor is not smaller than 10 AWG copper or 8 AWG aluminum.

(3) The grounded conductor [white wire] is insulated, or the grounded conductor is uninsulated and part of a Type SE service-entrance cable and the branch circuit originates at the service equipment.

(4) Grounding contacts of receptacles furnished as part of the equipment are bonded to the equipment [any built-in receptacles on your dryer have a ground connection (green wire) to the metal frame of the dryer].

In summary, you need to connect your green grounding wire to the white grounded conductor of your existing 3-wire receptacle, provided you meet all 4 of the above conditions.