It can be as easy as a scratch that just breaches the surface layers of skin. It isn't fun and can be quite painful. You really have to ignore it for it to get far enough for amputation, though depending on the strain of bacteria it can move quickly and need amputation within 2 days easily.
When this happened to me they weren't able to positively ID the bacteria that got me but I was still out of the hospital feeling a lot better within 8hrs with a 10 day prescription for Ciprofloxacin (used to fight anthrax) by the end of which I was fine. I don't think it's as hard to treat as they are making it seem in the article and I think her doctors screwed her initially by giving her weaker antibiotics making it resistant.
You should always wash your hands after being in the tank anyway but the problem is when there is damage to the skin and it works it's way into the blood stream.
The doctor's must of not diagnose it properly at first, that it got this far.
As far as cleaning my hands, I always make sure that I wash with soap up to my shoulder after I put my hand/arm in the tank. Having a 22" deep tank, the arms always get wet.