What's the name of the screwdriver that will open up an iPhone 4?
They are called Pentalobe screws and look similar to this picture from Wikipedia:



You can find compatible screwdrivers on iFixit or Amazon. If you do go with Amazon, though, make sure you read the reviews before you buy anything, since many of them are filled with complaints about the product not working.

There's even a guide which will show you how to replace the screws with normal phillips ones.