In order to get your page looking like the Oxygen Demo site, you'll need to follow some of the instructions which are included on the Theme page for Oxygen:
Specifically, you'll want to pay attention to this section:
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.
The Showcase Page template offers a featured slider for up to six Sticky Posts. To use the template, create or edit a page, and assign it to the Showcase Page template from the Page Attributes module. If you’d like use the Showcase Page template on your front page, go to Settings → Reading and set the Front page option to Static Page. Select the page you just assigned the Showcase Page template to as your front page and then choose another page to serve as your blog page.
This should set it up for you!