Once you have the primary (red) map pin where you want it (which you might do either by dragging and dropping, panning and re-centering, or by searching for a place name), you can save that location by navigating to the Locations page (click the link in the header), and then clicking the Add button:

If you want to save the position of the secondary (grey) pin, then here's the trick: on the map, click the Swap pins button:

The red pin is now at the grey pin position and you can save it as described above. (Saved locations can be used to set either red or grey pin.)

Read more: Using TPE Desktop Web App, Part 5: Locations