Insert Featured image and 2 Column No Sidebar Homepage

Hello,
I am looking thorugh the CODEX, and I cannot find how to add featured image support to my theme. I am in the middle of creating a custom theme for my website’s blog. I am having two issues with creating the theme. I want to have the the featured images (of varied dimensions) on the index page (featured articles).

The other issue is that I want to create a 2-column NO SIDEBAR layout. There will be 2 equally spanned columns. I created an HTML/CSS template here https://fkriii.com/smodel/ I want to feature many blog posts like this, however, including the header images. What is the best way for me to do this.

Thanks so much,
Zach

[No bumping, thank you.]