When writing a post, click the "Set Featured Image" link in the "Featured Image" meta box. This will open your media library. Select an image or upload a new one, then save it.
Typically, your image will be displayed using its default size, but depending on your theme, there may be additional cropping (cropping the image based on the theme's designed height/width) or display options (such as stretching, covering, etc.). Please refer to your theme's documentation to find these settings, although they are usually located in the customizer or theme panel.
