When you copy stuff from the Internet, you not only get the text, but you get all the styling that goes along with generating that text. If you paste that blindly into Pages with CMD+v, then you retain the styling which will give you funky output.
You have a couple of choices. One is to Paste with Match Stlying/Formatting or whatever they call it. The shortcut will be something like OPTION+SHIFT+CMD+v (add a couple of buttons to press and you'll need your toes to actually paste something..
)..or of course right-click and choose that option.
If that isn't doing what you want and you REALLY only care about the text itself. Open up TextEdit and then paste the content in there. Now from the top menu, choose Edit->Make Plain Text or Format->Make Plain Text (not in front of my computer, but it's something like that) to remove all formatting. Now you can safely CMD+c and CMD+v this text into Pages and not have it show up in any special way..