I have a dryer with a 4 prong plug but the plugin is a 3 prong. How do I wire up a 3 prong cord to the dryer. Or how do I wire a 4 prong plugin into the existing 3 prong plugin.

You can change the cord to 3 wire, by reconnecting the Ground/Neutral strap on dryer terminals.
New construction and remodel require 4 wires,
2 Hots, a Neutral and a Ground, All Number 10's. If in Metal conduit, that can be your Ground.