You can apply look and feel changes using Google CSE admin page. You can find screenshots about it here:
Google Custom Search field and button contain more css elements, so I cannot write a html id or class. But if you right click on the appropriate html element in your browser and chose “Inspect element”, then you can see the html code and find the class names or ids. If you move your cursor on the html code, the corresponding html element will be highlighted in the browse.
Sometimes it is not so simple, your site designer may help you.