In my experience from the field i see multiple ways and methods of customers changing their IP's. The most common error most make is running a software program to clone and or change their MAC on their NIC. This almost never works because the software needs to start when your computer starts.. And if your LAN service connects BEFORE your PC is started then your old MAC was submitted for the IP and not your new MAC.
The most effective way i have seen is to use your router or gateway (router aspect) to clone the IP of that device. Just like alex has mentioned. (For those using gateways if you manage ((and it's possible) to clone the MAC of the gateway itself then don't expect to get online
)
BUT... if you are using this as a way to get around megavideo's 72 min limit or get onto that gaming server that banned you then no problem. If you have done electronical damage to a company or anyone who cares enough to file a computer crimes police report then, Cloning your MAC and changing your IP will NOT hide your tracks. The backend will still have a record of the last X IP's assigned.
What i always done was unscrew Coax, p/c, verify 169 IP, connect coac, p/c, verify valid IP (Direct connection)
Or Exactly what alex said when using a router.
And a gateway, really depends on the version you have