I think part of the answer lies in the type of response you wish to evoke from the players (and the characters).
Are you wanting the PC's to be overwhlemed by a rare occurrence, or are these types of encounters more run-of-the-mill in your game?
If it's a common occurence, then it would probably be easiest to have the diety (or even an avatar ) announce his/herself and be done with it.
A rare encounter would be mind-blowing, once in a lifetime experience, something not easily forgotten or hard to mistake for something else. The diety may seem different to all the pcs based on their personal beliefs. You could play on that and sort of make it a surrealistic encounter with all sorts of supernatural goings-on ( flashing lights, sparks of energy, maybe tunnel-vision on the PC's end, gusts of wind or any number of other strange effects) to
highlight the scene.