When working on a post, click the link to “Set featured image” in the “Featured Image” meta box. This will open your media library. Either select an image or upload a new one and save.

Typically your image will be displayed using the image’s default dimensions, but depending on your theme there may be additional cropping (which cuts the image based on the height/width of the theme design) or display (stretch, cover, etc) options. Reference the documentation for your theme to locate these settings, though they’re often in the Customizer or a Theme Panel.