Someone asked earlier about CDTA, and that shouldn't be relevant to someone who has already has a ticket, since Amtrak is (I assume) taking care of bus arrangements. But it might be relevant to someone who's trying to get to central or western New York and can't get there.
For instance, I looked for ticket on Aug. 2 from Schenectady to Syracuse and found one, but couldn't book a ticket from NYP to Syracuse. So an enterprising person might take an earlier train to Rensselaer, take CDTA to Schenectady and join the Lake Shore Limited there, though it's going to be quite a headache to do so.
It is not an easy trip on CDTA. There's no direct connection. You take a bus to downtown Albany and transfer to another bus (I do this often when I fly out and take the train back, and it's about an hour and a half between the train station and the airport). The problem is, the CDTA trip planner wants you to use Empire Service to get between the two stations, which is, or course, no help at all, so you have to break up the trips to figure out the bus route.