Please consult the detailed theme description here http://theme.wordpress.com/themes/oxygen/ There are also many threads that explain how the Oxygen theme is designed to operate.
In Oxygen you can either have a Home page that displays your posts or a static front page ie. a Showcase template. http://en.support.wordpress.com/pages/front-page/#setting-up-a-static-front-page
Page templates can be set under the "Page Attributes" section on the page editor screen. For more information on Page Attributes:
Showcase page template
When you first activate Oxygen, you’ll see your posts in a traditional blog format but if you’d like to showcase your content in an online magazine-like fashion, then you can use the Showcase Page template. ...
Post thumbnails are 470 pixels wide, unless you make the post Sticky to show off in the featured slider, in which case they’re 750 pixels wide. Keep in mind: if you mark a post as Sticky but the featured image is less than 750 pixels wide, then it won’t display in the slider and will still disappear from the river of posts.
Please be aware that you cannot crop the sticky post thumbnails.
Sticky post thumbnails are 750 pixels wide in the featured slider
Regular post thumbnails are 470 pixels wide
If you don't see the page attributes module then make sure that you don't have it hidden in your screen options http://en.support.wordpress.com/screen-options/