download image from remote source and resize then save

You can try this:

<?php    
$img = file_get_contents('http://www.site.com/image.jpg');

$im = imagecreatefromstring($img);

$width = imagesx($im);

$height = imagesy($im);

$newwidth = '120';

$newheight = '120';

$thumb = imagecreatetruecolor($newwidth, $newheight);

imagecopyresized($thumb, $im, 0, 0, 0, 0, $newwidth, $newheight, $width, $height);

imagejpeg($thumb,'/images/myChosenName.jpg'); //save image as jpg

imagedestroy($thumb); 

imagedestroy($im);
?>

More information about PHP image function : http://www.php.net/manual/en/ref.image.php

You can resize keeping the ratio of image

$im = imagecreatefromstring($img);

$width_orig = imagesx($im);

$height_orig = imagesy($im);

$width = '800';

$height = '800';

$ratio_orig = $width_orig/$height_orig;

if ($width/$height > $ratio_orig) {
   $width = $height*$ratio_orig;
} else {
   $height = $width/$ratio_orig;
}