need help with power reduction

I have a power over ethernet switch running into a 3Com IP Phone poe splitter, with an output of 24V 1.2A DC, and need to have 12V 1A DC running into a wireless router. I assume that a simple zener diode/resistor series would take care of the problem but i am new to electronics and am having a little trouble designing the schematics of it. Any input would be greatly appreciated.

It sounds like you'd like to use the output of your 24 vdc supply as a source for a 12 vdc supply. If you aren't going to connect anything else to the 24 vdc supply then it seems that there is enough power -all you have to do is reduce the voltage. If you have something else connected then you'd have to indicate how much current is being drawn by all of the loads on the 24 vdc supply. Note that sometimes a mfr will indicate that a 1 amp supply is needed when the actual load is quite a bit less. In this case the sum of all the loads must be less than 1.2 amps, if that's the limit of your suppy.

If the 24 vdc supply has enough capacity then one way of getting to 12 volts is with a linear regulator like an LM317 - look up the National datasheet and there are plenty of schematics there. A heat sink is probably a good idea. A zener could be used but would need a power transistor to handle the load. I'd stick with the LM317 because it's probably lower in cost than a zener and transistor. A 7812 linear regulator would also be likely to work. There are many other ways to do this.

Note that you've not mentioned anything about regulation or ripple. Those may not be issues in this case but could be things to check.