If you have an oversized item (a wheelchair, bicycle, etc.) it will be in a little room to one side of the carousel, and you talk to the guy in charge of the room. Your bag will also be there if somehow your bag beat you to LA. (This happens if you take a scenic route from Chicago to Los Angeles -- for instance, Empire Builder and Coast Starlight -- but checked your bag through. The bag will take the direct route.)
Fair warning, the luggage handling people in LA can sometimes have a very, um, "manana" attitude, so if nobody's there, you may have to wait for an hour, or go find someone to page them. This shouldn't happen if your bags were on your train with you and you pick them up along with everyone else, but if something funny happens (for instance, if your bag arrived on a different train) it can be an issue. I had to deal with that.