Enough is to define image URL for logocontrolbar option. If you wish to have clickable image, you must also define a link URL for the logourl option if it is not already defined.
Logo height in controlbar fits other icons height, centered vertically. If the original image is higher, it will be scaled to the maximum possible height. Have a look at Nuevo plugin code setup.
Code snippet
<script>var player = videojs('example_video_1');
player.nuevo ({
logocontrolbar: '//domain.com/path/to/logo.png',
logourl: '//domain.com'
});
</script>