These assume your connection uses DHCP. If you have an assigned IP, ignore this post. Also, if these hints don't make it clear what to do, then don't try them.
If you have a router between your computer and your internet connection device (cable modem, DSL modem, etc), you would log into the router and renew the WAN IP address. Since there are many different routers, you would need to read your router's documentation.
If you don't have a router, not even one built into the internet connection device, you would go to a command prompt to renew the DHCP address of your computer. For Windows, this is "ipconfig /renew", assuming you have only one network connection on your computer.