It appears you have some kind of "caddy" on that computer. At least with Dells you have to remove a couple screws the slide the caddy out. From there you remove some more screws, remove a little connector on the end, and the drive is free. Reverse to rebuild.
As for what drive, it seems you're limited to PATA/IDE/44-pin drives (different names for the same thing). They aren't very common now-of-days so you may have to search for one on ebay or something.
As for getting the drive working, perhaps the easiest way would be using an external CD-ROM of some sort. However, if you have a pair of converters, you could probably mirror the old drive to the new one with software such as Ghost. Free imaging programs are also available from hard drive manufacturer's pages.