I used a 2-tool approach. A metal spudger to wedge the case open just the tiniest bit and get the job started (iPod video). Then the black one mentioned above ($2.95 from iFixit) to go all the way around. The metal may have dinged the very inside edge of the plastic case, but it can't be seen except on closest inspection. Both tools have survived to make other repairs.
The real trick is to be relax, focus and take your time.