How is it possible for a group of computers in the same office or home browse the same websites using one public ip address?

I t will be done by using PAT (Port Address Translation). During PAT, each computer on LAN is translated to the same IP address, but with a different port number assignment.

PAT attempts to use the original source port number of the internal host to form a unique, registered IP address and port number combination. For example, two hosts that have been assigned the IP addresses10.10.10.100 and10.10.10.101, respectively, could send traffic to and receive traffic from the Internet by using the single public IP address123.45.67.89. If that port number is already allocated, PAT searches for an available alternate source port number. Therefore, the host at IP address10.10.10.100 could access the Internet by using the public IP address and source port combination of123.45.67.89:10000. Meanwhile, the host at IP address10.10.10.101 could access the Internet by using the IP address and source port combination of123.45.67.89:10001.