I used to have quick icons at the bottom of the screen I could press to start my favorite applications
such as

firefox
terminal
screen capture

I've tried a lot of experimenting with this, but I can't figure it out.

If you can help with this, I would appreciate it.

Thanks!

Best regards, Howard

If you are using the standard task manager widget you should be able to right-click on an open application's entry in the task manager and check "Show a Launcher when not running".
Similarly, you should be able to browse to the application in the menu, right-click and select either "Add to Panel" or "Add to Desktop" to create a new launcher icon on either the panel or desktop, respectively.
You may also be able to add a Quick launch widget and add application launchers in there (I'm not sure off-hand if it comes with the desktop or has to be installed separately)