How do I wire a newer four prong dryer outlet to replace an older three prong outlet?

You'll need to open the outlet box first and see how many wires are in it. If you have 4, red, black, white and a bare or green ground then you are all set. Red and black go to the L1 and L2 connections, doesn't matter which. White goes to N and the bare or green to G.

In an older home, if you have only 3 wires, black, white (may be marked black or red), and a ground in the box then you can't do this. You can call an electrician to run a new cable to your dryer or you can replace the cord on the dryer with a 3 prong version.

Hold it! You cannot just swap out line cords.

If the new dryer is not designed to handle a three wire connection, you must change the circuit from a 3 wire to a 4 wire all the way back to the panel. Also, you must use the correct AWG (size) Conductors. For example, a 30 amp dryer would need to have 10/3 AWG conductors.

On the older 3 wire setups both the Equipment Grounding Counductor and the Neutral were tied together.

On 4 wire designs, neutral and ground are designed as separate connections.

In part to meet the current code that the only place that the EGC and Neutral can be bonded together is the main service panel.

If you do not match the new connections correctley, you could end up with a difference of potential between the dryer skin and the grounded conductor (Neutral).

This can have shocking consequences!

You're right Don. I should have let him know that.

Check the directions that came with the dryer, some are convertible, some aren't.

If it's not convertible you'll have to do as Don said, change the dryer feed all the way back to the service panel.