It's like a mental double-take. I experience no physical symptoms apart from a puzzled look on my face and a moment's hesitation to process the phenomenon.

No smart-assery intended: If you continue to feel dizzy enough to have to hold on to something, even if it's not every time you experience deja-vu, please see a doctor. Low blood pressure could cause this, and though it itself needn't be serious, the concussion you might get if you fall would be. Low blood sugar, too. It could also be a marker for some neurological issue -- probably not (don't scare yourself with Dr. Google), but dizziness shouldn't be brushed off.