I am not exactly sure what you are asking. For a web page, it's always the page
itself that controls the layout. The browser only sets the parameters. The page can choose to respond to those parameters.
For example, consider a page with a number of very important buttons. The page can choose to display two buttons a row when it detects the browser window is wide (as typical on a desktop computer), and display only one button a row when it detects the browser window is narrow (as typical on a phone). In this case, the parameter the browser is setting is the browser window width, it's the author of the page that decides to respond to this parameter to make it look nicer on narrower screens. It's the same concept when you print the page. The printing process set the paper width parameter but the page has to respond to it.
On the other hand, the page author of course can choose to ignore this parameter and the user would just have to scroll the page horizontally on small screens, or the print out will be cut off on the right when the page is being printed on narrower papers.
A lot of such adjustments are automatically done by the HTML element you use. For example, a simple <p> element will always wrap the text automatically depending on page width. You don't have to explicitly do anything. However if you use a table, then it may not work the way you wanted. In this case obviously you will have to adjust your HTML to get the result you wanted.
So the short answer to your question is, whatever you want to do, you do it inside your web page.