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When playing against Stasis Snare, I don't seem to be able to react after the ETB trigger resolves and a target is shown.

When the spell is cast, I can respond, but if I click "done" to move to the next action, I think what should happen is the ETB trigger should then go on the stack and I should get to see the target of the spell, and have another chance to react. Right now it seems to just execute the trigger without that, unless I'm doing something wrong? If I click "done" to the spell being cast, it just goes ahead and executes.

This leaves me unable to react unless I do so prior to target declaration, which means I can't sac the target in response or things like that. It's possible I'm confused but it's happened a couple of times and I don't see what I'm doing wrong. Anyone else have this issue? Am I just a dumb newbie (well, I am, but is that the whole answer this time)?

If you see the Stasis Snare triggered ability (on the stack), it's already on the stack and the target is selected by the controller of the Snare.
You should see the target in the game log and also if you move your mouse pointer over the Stasis Snare on the stack with the target arrow pointing to the selected target.

So if you push the "Done" button (while the ability is shown on the stack) you already pass your priority.
If you want to respond to the target selected you have to do it as you see the ability on the stack and you have priority.

I guess you were not aware how you get information about the selected target?

Well, I don't think I am seeing the triggerred ability. I see it cast, but with no target information in the game log and no target arrow. If I pass priority at that point (hitting done), the spell just seems to execute without giving me another round of priority.

I dunno. Maybe I'm hitting done twice or something (sometimes the UI is a little... sticky... that way), if no one else is seeing this it's probably me.

What you see first is the casting of the enchantment. That is without targets, because the ability that exiles a target does trigger as the Statis Snare does enter the battlefield.
So a second time something is on the stack, you can easily distinguish it by the added T-Symbol for triggered abilities on the stack in the left upper corner of the card image on the stack.

See the ability on the stack on the screen shot (targeting one of my creatures, me having priority).

Hmm. I must have double clicked done or something then. Thanks folks. I'll pay more attention next time and see.