If you see the image, the icon to enable 'Limit selection to visible' is not there.
Am I missing something?
You're in Wireframe shading mode, where the Limit Selection to Visible button would have no effect (as all vertices are visible all the time, so there is nothing to limit to). Change to one of the solid shading modes and it will return:
I am also new to Blender. For me I found that the icon came back when I went into edit mode from object mode. It was not visible in shaded object mode - This could help clarify the above response (as I could not see this in the shaded mode). I spend a long time trying to find this icon or a way to enable it through text input. I am surprised that this does not come up as a searchable command in the text input box (brought up with the space bar) even when in edit mode.