Next you will find the code with comments for each action. Please read them carefully.

  <?php
 //define a maxim size for the uploaded images
 define ("MAX_SIZE","100"); 
 // define the width and height for the thumbnail
 // note that theese dimmensions are considered the maximum dimmension and are not fixed, 
 // because we have to keep the image ratio intact or it will be deformed
 define ("WIDTH","150"); 
 define ("HEIGHT","100"); 

  // this is the function that will create the thumbnail image from the uploaded image
 // the resize will be done considering the width and height defined, but without deforming the image
 function make_thumb($img_name,$filename,$new_w,$new_h)
 {
 	//get image extension.
 	$ext=getExtension($img_name);
 	//creates the new image using the appropriate function from gd library
 	if(!strcmp("jpg",$ext) || !strcmp("jpeg",$ext))
 		$src_img=imagecreatefromjpeg($img_name);

  	if(!strcmp("png",$ext))
 		$src_img=imagecreatefrompng($img_name);

 	 	//gets the dimmensions of the image
 	$old_x=imageSX($src_img);
 	$old_y=imageSY($src_img);

 	 // next we will calculate the new dimmensions for the thumbnail image
 	// the next steps will be taken: 
 	// 	1. calculate the ratio by dividing the old dimmensions with the new ones
 	//	2. if the ratio for the width is higher, the width will remain the one define in WIDTH variable
 	//		and the height will be calculated so the image ratio will not change
 	//	3. otherwise we will use the height ratio for the image
 	// as a result, only one of the dimmensions will be from the fixed ones
 	$ratio1=$old_x/$new_w;
 	$ratio2=$old_y/$new_h;
 	if($ratio1>$ratio2)	{
 		$thumb_w=$new_w;
 		$thumb_h=$old_y/$ratio1;
 	}
 	else	{
 		$thumb_h=$new_h;
 		$thumb_w=$old_x/$ratio2;
 	}

  	// we create a new image with the new dimmensions
 	$dst_img=ImageCreateTrueColor($thumb_w,$thumb_h);

 	// resize the big image to the new created one
 	imagecopyresampled($dst_img,$src_img,0,0,0,0,$thumb_w,$thumb_h,$old_x,$old_y); 

 	// output the created image to the file. Now we will have the thumbnail into the file named by $filename
 	if(!strcmp("png",$ext))
 		imagepng($dst_img,$filename); 
 	else
 		imagejpeg($dst_img,$filename); 

  	//destroys source and destination images. 
 	imagedestroy($dst_img); 
 	imagedestroy($src_img); 
 }

 // This function reads the extension of the file. 
 // It is used to determine if the file is an image by checking the extension. 
 function getExtension($str) {
         $i = strrpos($str,".");
         if (!$i) { return ""; }
         $l = strlen($str) - $i;
         $ext = substr($str,$i+1,$l);
         return $ext;
 }