I moved into a house that has a 4 prong outlet and my dryer has a 3 prong cord, how do I go about changing the cord. I called an electrician put the job is to small for them to come. My manual only has about the where to put the neutral and the grounding wire but does not explain which screw to put the red and black wire on. The neutral wire is in the middle so can someone tell me if the red wire goes on the left or right of the neutral screw and the black one also on the right or left. All screws on the dryer are silver with no color markings

It does not matter which tap handles either hot conductor. Red and Black are your hot conductors.

The big change in a three to four wire conversion is the proper placement of the Neutral (white) conductor and the Ground (green) conductors.

On a three wire system, Neutral and Ground can be connected together. On a four wire system that cannot be together.

The reason for the change is because the NEC only allows Neutral and Ground to be bonded together at the Main Service Panel or Main Disconnect Switch.

If they are tied together else where, that objectionable current may be seen and other locations.

On a 3 wire dryer, the 2 outside terminals are usually the hot, The center terminal will likely have a white wire, leave that on the terminal, and connect your white from the 4 wire cord to that center terminal. On the center terminal, you may see a metal strap that folds up onto the center terminal, remove that strap, then where the strap connects to the case of the dryer, connect the green to that screw which held the strap.
Ranges are basically the same.