How can I remove the glass domes from my light fixtures?
This looks like fixtures I have had, which are held in place by three screws.  It's hard to be certain from the photo, but if it is like this, then you should loosen the screws by hand bit by bit until you are able to remove the globe.  That should expose the bulb and the socket it's screwed into.

If not, then please climb up higher to take a photograph that shows the part of the globe that comes closest to the ceiling.