How do I install a Leviton light switch timer?
First off, if there's not a grounded (neutral) conductor in the box, you cannot connect this device.
Based on your description of the wiring, it's difficult to tell exactly how your current switch is wired. If you're not sure yourself how the current switch is wired, it might be best for you to contact a local licensed Electrician to install the switch for you. If you have a basic understanding of your wiring; and/or electrical wiring in general, the following information (which can be found in the instruction sheet that came with the device) should be helpful.
Single pole installation
If this is a single pole installation (only one switch controls the lights), then you'll only need to connect 4 of the 5 wires.

Black connects to the ungrounded (hot) conductor feeding the box.
White connects to the grounded (neutral) conductor feeding the box.
Green connects to the grounding conductors.
Red connects to the load (lights).
Yellow/Red is capped off and not used.



Leviton Instruction Sheet

3-Way wiring
This device is not compatible with standard 3- or 4-way switches. If you're going to use it in a 3- or 4-way setup, you'll have to purchase compatible vizia +™ on/off remotes.
3-way wiring with coordinating remote switch (VP0SR-10)
If you're pairing the timer with a coordinating remote switch, you'll wire it as follows.

Black connects to the ungrounded (hot) conductor feeding the box.
White connects to the grounded (neutral) conductor feeding the box.
Green connects to the grounding conductors.
Red connects to the load (lights).
Yellow/Red connects to the wire that will be connected to the yellow/red terminal of the remote switch.



Leviton Instruction Sheet

3-way wiring with matching remote switch (VP0SR-1L)
If you're pairing the timer with a matching remote switch, you'll wire it as follows.

Black connects to the ungrounded (hot) conductor feeding the box.
White connects to the grounded (neutral) conductor feeding the box.
Green connects to the grounding conductors.
Red connects to the load (lights).
Yellow/Red connects to the wire that will be connected to the yellow/red terminal of the remote switch.



Leviton Instruction Sheet