IMDb is right--although the episode refers to the drug that the girl was using as 'speed', it really appears to be LSD (or perhaps mushrooms or mescaline or some other psychedelic drug). Speed literally speeds up the metabolism and behaviors and it's also commonly referred to as 'uppers'. Not a huge mistake (as either one can be quite nasty) but considering that the entire episode is about the drug, they should have done their research.
The episode begins with a young lady standing on a rock ledge. She's having a 'bad trip' and Danny responds to try to talk her back to safety. However, she's in her own little fantasy world and ends up jumping to her death--300 feet into the sea and rocks below.
Afterwords, Steve decides that due to a recent rash of 'speed'-related deaths that the forces of Five-O must be used to get to the heart of the problem. The trail leads to a freakedelic professor (Ed Flanders)--an obvious Timothy Leary-inspired character. The professor seems to feel no responsibility for her death--blaming it on society!! The only way to get evidence they need on the guy is to infiltrate his little inner circle. However, in the meantime the dead girl's father is running amok--demanding SOMETHING be done immediately. See the episode for yourself to see what happens next, but let's just say that Danno becomes a real hep-cat in order to try to end this drug's reign of terror (personally, I would have chosen Chin Ho for this assignment--he doesn't get do too much on the show and is the epitome of cool).
Overall, this is one of the poorest episodes of season one for several reasons. As mentioned at the top, the writers should have gotten the facts right if they were writing an episode about drugs. Second, the show was really, really goofy--with lots of silly psychedelics and plot. Never was it particularly believable and it just comes off as contrived and very weak.