It is not a dumb question. I sat in the living room with my new road bike for a while before I figured that one out. (I did not get it at a shop.) I agree that the shop should have gone over this with you.

If you're like me, you've first figured out that pushing the smaller black lever did something (like shifting up, if it's on the right side). To downshift (on the right side, still) you have to push the whole thing (the small lever and what you've been thinking so far is primarily the brake) toward the inside. It takes a bit more reach and it's not as intuitive at first.

On the left side, pushing the small black lever towards the inside will make you shift into an easier chainring. Pushing the whole thing makes you go on a bigger chainring (increasing the resistance). So it is the opposite.

Why such a confusion? Basically when you press the small black lever (on either side), you always go from a big cog or chainring to a smaller one. It's easy for the bike to do that because it's like going down stairs. However, when to move to a bigger cog or chainring, you need more strength/leverage because it's like going up stairs. That's why you use the bigger lever. [This is not a very accurate way to describe it, but it helped me understand what was going on.]

Good luck, and please come back to tell us about your riding stories!