Choose points in left-hand side panel to add them to the k-d tree. When you want to toggle to search-mode, just click on the appropriate button, then click on a point to search for on the left-hand side. To switch back to insertion-mode, click on insert. Restart clears the two panels and restarts the demonstration in insertion-mode.
Also note the presence of a pop-up window which will report your mouse position in order to make point placement somewhat easier