There are a number of ways to monitor the usage of the Moodle site. Moodle has a comprehensive logging system, which provides a great audit capability through the provision of a suite of standardized reports. In addition to the logging and reports, Moodle also presents some basic statistics on general usage that can help an administrator understand how the site is being used.
Statistics need to be enabled for the site by an administrator, and preferably should be configured to run at quiet times, say, very early morning.
Statistics can also be run manually by an administrator, but note that this will take a while to process completely.
Once they have been compiled, they can then be viewed by navigating to Administration | Site administration | Reports | Statistics.