You want to prevent all remote network connections, incoming and outgoing, on your network interfaces.
To shut down one network interface, say, eth0:
# ifconfig eth0 down
To bring up one network interface, say, eth0:
# ifconfig eth0 up
To shut down all networking:
# /etc/init.d/network stop
# service network stop Red Hat
To bring up all networking:
# /etc/init.d/network start
# service network start Red Hat
Linux provides three levels of abstraction for enabling and disabling your network interfaces (short of unplugging the network cable):
The lowest level, to enable/disable a single network interface. It has other functions as well for configuring an interface in various ways.
This mid-level pair of scripts operates on a single network interface, bringing it up or down respectively, by invoking ifconfig with appropriate arguments. They also initialize DHCP and handle a few other details. These are rarely invoked directly by users.
A high-level script that operates on all network interfaces, not just one. It runs ifup or ifdown for each interface as needed, and also handles other details: adding routes, creating a lock file to indicate that networking is enabled, and much more. It even toggles the loopback interface, which might be more than you intended, if you just want to block outside traffic.
The scripts ifup, ifdown, and network are pretty short and well worth reading.
ifconfig(8). usernetctl(8) describes how non-root users may modify parameters of network interfaces using ifup and ifdown, if permitted by the system administrator.