We did the Liberty Cruise while visiting from Alaska. Tip: get your tickets online, so you don't have to stand in line when you get there! Once they check your tickets, you load onto the boat - this includes climbing stairs - to their open deck. It's best to get a seat on the end so you don't have peoples' heads in your photos if you don't plan to get up and walk around inside or on the front of the boat. They do not allow you to stand in the main area where the chairs are - you need to go inside or to the bow - so that you're not blocking other people's views, hence sitting on an end.
There is a guy who narrates the cruise with history and whatnot. He was entertaining. Once you leave the dock, if you want to get up, you can go stand inside near concessions or at the front of the boat for photos. The narrator guy tells you when you're approaching landmarks and bits of history about them. They do sit in front of the Statue of Liberty for a little bit but not too long. They also turn the boat so everyone can see.
There is a bathroom in the lower part of the boat, which was clean.