The first steps of modifying mesh is to select the target, not in the level of GameObject/Component, but in the level of vertices.
Mesh-Manipulator provides many ways to select vertices in target mesh, including click selection, border selection, All/None selection and loop-selection.
You could use the most appropriate methods according the use-cases.
Now, let's examine them one by one.
The most basic selection method is to click on the vertices (abbr. vert).
You might already notice that when Mesh-Manipulator is activated,the edge of mesh faces is drawn in black on the mesh surface. (the face edges are already processed by trying best merging overlapping vertices & merging triangles to form quads)
If you click on a vert, it will become selected and tinted yellow, meanwhile all other verts are deselected;
To add/remove vertices from selection, hold the "shift" and click vert, it will toggle the selection state of specified vert;
Be sure to remember that "shift" can be combined with all the other selection methods too.
We could use hotkey "Z" to toggle transparent mode, in which the mesh's material is changed to transparent and we can select the vert at the back side.