Watch the videos in System Preferences -> Trackpad & Mouse to learn more about gestures and to set up your trackpad the way you want to use it.
On mine, which is set to "tap to click," I would tap on the icon in question, ask myself if I am 100 percent sure I want to delete it, then use three fingers to "drag" it to the trash OR two finger tap to "right click" and select "move to trash."
To select an address in Mail: again, use three fingers to swipe-select, and the backspace key to delete.