Press Ctrl+A then : and then type
scrollback 10000
to get a 10000 line buffer, for example.
You can also set the default number of scrollback lines by adding
defscrollback 10000
to your ~/.screenrc file.
To scroll (if your terminal doesn’t allow you to by default), press Ctrl+A then Esc and then scroll (with the usual Ctrl+F for next page or Ctrl+A for previous page, or just with your mouse wheel / two-fingers). To exit the scrolling mode, just press Esc.
Another tip: Ctrl+A then I shows your current buffer setting.