A small knife or very small screwdriver is the best tool. Helps to have 2 of them, sometimes. The outer case is pretty flexible.
All you're really after is a brief re-flow of each solder joint. The cracked joints exhibit a faint visible dark ring when viewed under some magnification.
Most hobby solder irons are powerful enough to heat each joint properly. Make sure the iron is all warmed up before starting work. YOu usually don't need to even add any solder- there's plenty on the board. Just make sure the iron is nice and clean ( a damp kitchen sponge works really well) or maybe add a little flux to improve heat transfer.

You should also be careful that some of the copper parts will get hot after soldering- avoid holding onto anything but the plastic base.

Good luck!
Rob Bareiss -- 15 years of electronic soldering experience
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Rob Bareiss, New London CT ::: "Roterande Fläkt Och Drivremmar!"