First open up your internet browser and type in the url to get to your router settings page. Such as with a linksys router, would be 192.168.1.1
I will demonstrate this with a DD-wrt firmware, which is different than the default linksys router firmware.
You're going to have to navigate yourself to the mac address page. With me, it's called "mac address clone"
With me i set it to enable and it shows my mac address twice. On the second one, simply change a character or two and click apply/save.
You're going to notice that your internet will stop and you have to unplug and plug your router in. once you connect to the internet again you should have a different ip address.
Not all of our routers are the same so things are going to be a bit different for you, unless you have the same firmware that i do.
I hope for anyone trying this that you will be able to do this. I used to think it didn't but i tried yesterday and it did.