What kind of events?
If it's an event that can be set up to be triggered for all records in contacts, the script can then check data in the current record and do nothing if a field or fields in the contact record do not have a particular value. That script could then either send an email to you or could set a value in a field in a table that logs such event notifications. Then a script on your system that is performed peridically can check for the appearance of new records in this table and pop up a message, custom window, play recorded audio file in a container...
Event like a reminder of certain things on particular time and date!
Say like, Visual alert and sound plays on specific date and time.
Example: I have a meeting with client A on Monday 12:00PM. i add this event into database and set alarm on 11:30AM. and do other things. as clock strike 11:30AM there should be message on Desktop to remind me of it. All this happens with Filemaker is running.
Take a look at the Install OnTimer Script step. While it is usually used to run a script at periodic intervals, it can also be used to "schedule" a script to run at a specific time and then the script can cancel the timer so that it does not run a second time.
To get the script to run at a specific time, you use a calculation for the interval setting in this script step that takes the time specified in the event record and subtracts the current time to get the number of seconds from now to when you want the notification to appear. When that script is run by the timer, a second call to install OnTimerScript with no parameters then cancels the timer so that it does not get tripped again.
The script thus performed can set values that cause conditional format settings to change the appearance of things on your desktop, it can pop up a custom dialog or new window with a message in the window and it can either use the Beep script step to sound your OS system sound or it can play a recorded audio file stored in a container to provide an audible alert.
The main limitation to this approach is that you can only set up one timer for any given window. If you have multiple events for which you need this notification, you either design your script to set up one notification at a time in the order that they appear or it must use the new window command to set up some windows (can be hidden, I believe) with one window for each notification timer.