While that page doesn't quite explain how the soaker was opened, it does give you an idea of how the case separates and what to look for when opening.
In terms of opening soakers, I've found a good Phillips (cross-head) screwdriver as well as a flat-head screwdriver (and sometimes also a exactoknife) are useful. The first step is definitely removing all the screws. One important thing to note is that often different sized screws are used on different parts of the blasters. Make sure to keep track of which screw belongs in which hole if you intend on putting the soaker back together after. (Of course, all water and pressure should have been removed from any soaker before attempting to open it)
After the screws are removed, the case should now be separatable to expose the internals. Sometimes parts of the case are glued/sealed somehow. That's where the flat-head screwdriver comes in handy i.e. pushing the head gently in where the case can be pryed apart slightly and twisting the head to further nudge the case apart until the stuck areas open.
After its open, the harder part is diagnosing the real cause of the problem and determining what to do next.
I'm sure others can also add in more info than the brief summary I gave above. Good luck!
