By default the Home page is the blog page and any new posts will go on this page. However, if you want to have a Static Home page then you have to create a Home page and then add your content and publish it.
For a blog page you have to create a blank page and name it what ever you want and then Go to Settings ->Reading -> select Static Page
for the Front Page select Home
for the Post page Select the blank page you just created
Now save your settings, and you will have a Home page that is static and a blog page that will have all your posts.