Adding without any selection
This is quite simple. When you CtrlLMB click without any element selected, you just add a vertex. This vertex is not linked to anything, it just floats in the 3D space. This happens regardless of the select mode you are using. However, in Edge or Face mode, you will not see the new vertex, and it will not be selected after creation. In Vertex select mode, it will be selected after creation, so if you continue adding new ones, you will be in the second case described below!
Adding with a previous selection
This is a much more complex situation. Shortly speaking, it is a sort of flat rotated extrusion.
Well, if you just have one vertex selected (and hence are in Vertex select mode), it is quite simple: your newly added vertex will be linked to the previously selected one, and the selection will be “transfered” to the new one.
As soon as you have multiple selected vertices, it’s more tricky. For each CtrlLMB click, there are as much new vertices as previously selected, each one linked to its “ancestor” – and only newly created elements are selected afterwards. But the location of these new vertices is not a simple translation of the selection, they seem to be somewhat rotated. I do not understand the underlying algorithm used here, so if someone know it, please edit this page!
If the selection contains edges (either explicitly in Edge select mode, or implicitly in Vertex one), these edges are extruded as well, creating new faces.
The same goes with selected faces – but with one more subtlety: as with face extrusion, the “original” face is deleted, unless it has no neighbor faces… And the “extrusion” is done in the view plane, not along the face normal!
So, for your own sake, you should only add new vertices, and with only none or one previously selected vertex!