Here's a very simple tutorial for you and it doesn't involve the old ipconfig /release and /renew method from ages ago.
1. Assuming you're using a router (most people do these days) you need to log in to your router. You can usually achieve this by typing http://192.168.0.1 or http://192.168.1.1 in the address bar, although your router's IP may differ.
2. If you have ADSL, you can usually just disconnect and reconnect via the router's control panel, but if you have cable you may need to read on. When you're logged in, look for something called 'MAC Address', but if it says 'MAC Address Filtering' do not touch it.
3. If your router supports MAC address changing, change the MAC address to something random, but always make sure the first part is 00 because I've encountered problems when I use anything other than that.
4. Save the settings.
5. Restart your router and modem at the same time.
I personally use this on my PH cable connection, hopefully you will get a new IP address with the same method.
Please use this at your own risk and don't forget to take a note of your original MAC address just in case.
I apologise for the lack of images, but there are too many types of router to cover everything.
Originally posted by i.Mark