On Red Hat systems it is /etc/sysconfig/network-scripts/ifcfg-Auto_ethN (where N is the NIC you want to set - usually eth0). You would edit that file to change the static IP address (IPADDR=IPV4address, such as 192.168.1.100 - you can't do this with DHCP) and then run the "service network restart". Bingo! Your address has now been changed.
For Ubuntu, you would go to /etc/NetworkManager/system-connections. Each NIC (hardware or WiFi) will appear as the file named "* connection N" where the leading asterisk is "wired" for a hardwire connection, and the trailing N is a number for the connection #, such as 0 for eth0, 1 for eth1, etc). I'm not sure what a WiFi would appear as since I am running this in a virtual machine without WiFi... :-)
In the appropriate file you will find the section [ipv4] and an entry "addresses1=YourIPV4Address;YourGatewayAddress". Example (from my VM):
So, change the IPV4 address (leave the gateway alone), and then, as mentioned above, restart the network services, except that for Ubuntu you would use "service restart network-manager" either as root, or with sudo. Oops. I mean "service network-manager restart"... :-) Danged keyboard keeps mistyping for me!