Things You'll Need
Noncontact voltage tester
Luthron three-way dimmer switch (incandescent or fluorescent)
Black plastic electrical tape
You wire three-way Luthron dimmer switches the same as all other three-way dimmer switches. They are wired in combination with one standard three-way toggle switch which allows the light to be turned on and off from two positions with the three-way dimmer switch controlling the lighting level. They are wired in combination with a standard three-way switch and one or more four-way switches, which allows the light to be turned on and off from three or more locations while the one three-way dimmer switch controls the lighting level.
Turn off the circuit breaker protecting the lighting branch circuit that you will be working on. If your home is an older home that still has the old Edison-Base fuse box instead of a modern breaker panel, unscrew the fuse for the circuit you will be working on. Remove the fuse completely to be safe, don't just loosen it a few turns.
Remove the switch cover plate. Loosen the two #6-32 "Captured" screws holding the switch in the device box and pull it from the device box.
Turn on the non-contact voltage tester and bring it close to the wires in the box. There may be other circuits passing through the box that are still energized and you need to be aware of this for your safety. You won't be working with those wires so there's no need to find the circuit breaker controlling them.
Remove the wires from the old three-way toggle switch. The black wire connected to the dark colored screw on the bottom of the switch is the wire bringing power to the switch. The red and black wires connected to the brass colored screws at the top of the switch are called "Travelers" and carry the switched power to the second three-way switch through any four-way switches located between them. The bare copper wire attached to the green screw, if there's one is the safety grounding wire.
Cut the stripped, looped ends from the wires and strip the insulation back ½ to ¾ inches. Dimmer switches come with pre-attached, color-coded pigtail leads that will be spliced to the circuit wires instead of screw terminals like regular toggle switches. You need straight wire to make proper splices.
Splice the black wire bringing power to the switch to the black pigtail on the dimmer switch. To make this splice, hold the stranded pigtail wire against the solid copper wire so that their ends are even and screw on a wire nut. Splice the red and black travelers to the two red pigtail leads on the dimmer switch. It doesn't matter which traveler connects to which pigtail.
Tug on the splices to make sure they are secure. Secure the wire nut to the wires with electrical tape. This step isn't required by Code but it's an extra step that professional electricians take for safety.
Install the dimmer switch in the device box. Install the new cover plate that came with the dimmer switch. Turn on the circuit breaker or replace the fuse you removed.
This is an exception to the rule requiring DIY electrician's to get a wiring permit and having their work inspected. This project falls under the remove and replace exception because you're simply replacing one switch with another, and aren't installing any new wiring or devices.