You can find those in the functions file. Depending on the theme you’re using, it should look something like this –
//* Add new image sizes
add_image_size( 'featured-content-lg', 1200, 600, TRUE );
add_image_size( 'featured-content-sm', 600, 400, TRUE );
add_image_size( 'featured-content-th', 740, 340, TRUE );
add_image_size( 'portfolio-thumbnail', 348, 240, TRUE );
So if you want to add your own size, just duplicate and rename one of the sizes above that already exist. The first number is the width, and the 2nd is the height.
“Also, what image size do you typically upload to the media library when working with a responsive template?”
I usually just upload the image at it’s regular size (large) and then whatever I’m using to display the thumbnail will automatically resize it if needed.