Add menus

Hi there, I have a few changes I would like to make to my site but I'm a bit confused about what I need to do. I'd like to modify my site so that the menu on the home/landing page is different from menus in other areas of the site. So, for example I would like to put two options on the menu on the landing page, and then when someone goes into either area they encounter two different menus and content. I am fairly certain it's possible since I see the option for "add a new menu" under appearance--> create a new menu. Can you please give me any tips how to assign the menus to different areas of the site? Thanks so much, Amy