how to automatically fit featured images to the frame-space in home page

Hi,
I am trying to implement a new theme to the website: ‘www.indileak.com’
How to make changes in the codes so that featured images get fit to the frame space allotted in the home page.

Is there any plugin that can automatically select the first image embedded to the post as the featured image and can automatically fit it in the frame space provided?

In the present theme I am using, this feature is working fine, but in the new theme it is not fitting. Where to change? Can anyone provide me the codes?