You might use that information:
CSS Print Media Query | Styling the Printable Version of your Site[
^].
Thus with CSS, it is possible to make some adjustment for printing.
Another possibility is for the server to generate some printable documents (often PDF), that the user can download and print. Many web site will do it that way.
As indicated in a comment, it is not possible to automatically print as otherwise it would be possible for spammer to print lot of stuff when you visit their sites. Thus for security reason, printing has to be explicitly asked by user through web browser UI. If printing was allowed, then it would probably be almost has bad has advertising on some web site...