To test the alert functionality, make sure you have at least one group, one contact (within that group), and a monitor with the specific group designated to receive alerts.
Then, go to Monitors > (sub-menu for a specific monitor) > Edit > Advanced. For "Expect Data", input a string that is not present in the response from a service being checked - for example, "asdf". Then, click "Submit". This forces the monitor to create a down event once it verifies that "asdf" is, indeed, not present.
Once you receive the test alert, simply repeat the process above to remove "asdf" from the "Expect Data".