Well you can use file functions but I think this way is easier:
$img = 'http://www.somwhere.com/images/image.jpg';
$img = imagecreatefromjpeg($img);
$save = 'images/image.jpg';
imagejpeg($img, $path);
I think that should work. If it doesn't you can use curl but this is easier.
This is a fairly good script. There are others. Do a search on this forum for something like "Website thumbnail" or "Website screenshot".