How to Open Housing to Replace Light Bulb?
I have a similar fixture, and it uses a spring loaded set of three clips.  Simply pull on the cover.  But for the ones I have the force is scary high for a thin diffuser. 

I also have a similar fixture and the dome has three bayonet tabs which will disengage with about a 1/8 turn.  This one is a bit older, and the diffuser is heavier than the one mentioned above.

Those are common fastenings, but there is no assurance that they are what you have.  If you know your manufacturer/model, you might find info with a product search.