You can go to Network in System Prefs then select your network and go to advanced... then click Renew DHCP Lease and that will have your router hand you a new local IP address, but if you are trying to change your public IP address that will need to be done by your Internet provider. Sometimes if you just unplug your cable/DSL modem a few minutes then restart, your ISP will give you a new IP address.
This varies by Internet provider though. I have had the same IP address for months on end even with power outages and cable modem reboots.