Final answer:
To enable AAA on a network device and define its method list, use the 'AAA new-model' command followed by 'aaa authentication' to configure the method list, such as 'aaa authentication login default group radius local' which uses RADIUS for authentication with local fallback.
Step-by-step explanation:
To enable authentication and define its method list with AAA (Authentication, Authorization, and Accounting) on a network device, you would use the AAA new-model command to first enable AAA globally. Following this, you would configure method lists using the aaa authentication command. An example command is:
aaa authentication login default group radius local
This command specifies that the default login should use a RADIUS server for authentication and, if it's not available, fallback to the local database.
Method lists allow you to define the sequence and methods through which authentication is conducted. Note that you might also need to configure other settings like the RADIUS server itself, key information, and additional AAA policies depending on your specific network requirements.