He would completely submerge the object in a pool of water, then recite his incantation/perform his rituals (I haven't really decided which yet) and the surface of the water would either smooth itself and reveal an image or rise out of the bowl/container to form the person and their surroundings (though again, I'm undecided which way to go). The significance of the object itself is that it must have some level of resonance with the person's soul, and that resonance is created by physical contact, or as you suggested great sentimental value combined with proximity. This would also mean that he couldn't scry animals, since they have no souls (just a side note).

Regarding the time it takes for the resonance to wear off, it would depend on how attuned the item was in the first place. If they only touched it once for a few seconds, he would have roughly that amount of time before it became useless, so it would more or less be a 1:1 correlation. The time could be reduced, however, if the item came into the possession of someone else, as it would then begin the process of developing a resonance with that new person's soul, erasing the resonance with the first as it did (so just him having the object to use for scrying would accelerate the decay of the resonance).