There are many ways to discover network topology and most of the ways you know determine your experience in the field. First, you can ping random IP addresses. If you do a tracert, you can discover router IP addresses. You can install a network traffic packet analyzer to read some of the traffic that passes between segments of the network. You can run an SNMP scanner and attempt to find open systems. Even at a basic level, you can plug a laptop into open data ports to see if you can connect to various servers and other desktops.