Staffs and Clefs

To add anything from the palette, the easiest way is to click where you want to add it (in this case, the existing clef), then double click the palette icon. You can also use drag & drop, but you have to make sure you wait until the target is highlighted before releasing the mouse.

This is documented in the Handbook - https://musescore.org/en/handbook/palettes. Also in https://musescore.org/en/handbook/clef-0, although the fact that clefs can be added via double click is brand new for 2.0.2 and not in the Handbook yet. Prior to 2.0.2, double click worked for most but not all palette elements, and clefs were among the ones that weren't supported.

To put it simply, if you want to change a treble clef part into a bass clef part and have all the music correspondingly shift and octave (or two) down, you would click on the existing treble clef at the beginning of the score, open the Clefs palette, and double-click the bass clef in the palette. (At this point, the clef would be changed, but the music wouldn't, and the notes would probably be on ledger lines above the staff.) Then, you would click on the first measure of the music to select it, [Shift]+[End] to select all the way up to the end, and [Ctrl]+[Down arrow] to transpose it down an octave.

Note that this could end up coloring some notes red to indicate that they're no longer within the instrument's range. To fix that, right-click an empty part of a measure or on the instrument name, choose "Staff Properties…", and use the "Change instrument" button at the right of the dialog that opens up to choose whichever instrument you like.

Clear enough?