As long it's a genuine xbox HDD, any HDD will work with the Xbox 360 Slim.
You just need to disamble ur Xbox 360 HDD, unplug the HDD from the port and voila insert it into ur slim.

There's other way to upgrade though i think.
You need to buy a Westin Digital Laptop HDD, then you need to flash to ur computer with certain software then u can put into ur xbox 360 slim.

However i don't recommend it even though it's cheaper than the 250GB + the size of HDD can go up to 600GB. Microsoft can ban you and will ban anyone who uses none of their genuine product on xbox