The theme you refer has a theme description here http://theme.wordpress.com/themes/stay/
live demo site http://staydemo.wordpress.com/
You will need to follow the instructions to make the theme to look like the one in the demo. The demo is using the "Home page template" which cycles through select top level pages on your site. Create a page called for example "Home" and then set that page as the static front page for your site and create another page fro example "blog" for your posts to appear on.
The front page of the blog by default will display your posts (not pages) in reverse chronological order, with the most recently published post on top. If you do not want all the posts to show on the front page, then you can create a static front page. To do that create two pages > http://en.support.wordpress.com/pages/ After you do that you go to > Settings > Reading and make the designation change and click “save changes”.
Front page displays
__ Your latest posts
A static page (select below)
Note 1: The theme has a featured page slider and image size is at least 960 wide. Ideal width for the slider is 1200px.
Note 2: You're not supposed to set a featured image to the page you've set as your front, and you're not supposed to include it in the pages you assign to the slider. http://en.forums.wordpress.com/topic/stay-theme-slider-and-featured-image-issue?replies=6#post-1485466