I'm rather boring about it.

If it's one not coming out of the box, I'll just look at it. If it's one I'm taking out and displaying, I'll first open it up and get a feel for it. Then, spend some time finding a particular spot to put it, making sure the light is all right and so on.

I smell them. I love the smell of new things.

I also look over them for any imperfections and then get annoyed when I find some and wish I hadn't looked for them, since they're so small I wouldn't have naturally have noticed but knowing they're there is enough to bug me forever.

I leave 'em in the box for a day or two to admire them, then I take them out and pose them. I'll probably change the poses of my other figures too. The first pose I put them in is one shown on the box, which I'll keep for a while as a reference for the next couple of poses.

Not really.

If it's a model kit though, I'll usually look up a bunch of gunpla tutorials to try to figure out how to paint it. Then I'll remember I have no money, regret buying it, let it sit for ages, and put it together minimally and unpainted eventually.

I take a bunch of photos of it, including the box.
then when I find a pose I'm happy with, I look for a decent spot to keep it.
Latter I edit the previously taken pics when I don't feel like doing much else, and eventually use them while reviewing the fig on my half-assed blog.
which of course no one cares about becuase the fig has already been out for a good while by then. (among other reasons)

latter on if I decide to change up the figure's pose, I'll possibly take more pics of it to update the old post I made about it.