First, there are the obvious methods of changing your IP address:
1] Connect to the Internet from a different location: this could mean using a dialup connection to connect through a different access number, or going to a free Internet cafe or a library with free wifi access, etc.
2] Ask your ISP the process for obtaining a new IP address on your connection. This process varies from ISP and ISP -- on very rare occassion it is as simple as turning your modem off for a few hours. But more commonly the process is more complex, and some ISP's actually make it nearly impossible. On my ISP, I have tried every process and trick I could find on the Internet -- nothing worked. They, like many ISP's these days, are pretty serious about maintaining a client's IP address.