For the Statue of Liberty, you have to take a cruise from either Battery Park (Lower Manhattan) or New Jersey. You have to book for tickets at least a few days beforehand just to be on the safe side, especially if you want to get to the crown of the lady. I was lucky that there were no long lines to get on the cruise when I went, because I was told that the lines can get as long as 2 hours on really busy days.
The tour and the museum really helped me get to know the lady so much, so much more than the celebrity that I saw on the TV often. It was definitely one of my highlights seeing this statue that symbolizes so much to those who dreamt.