Great advice.A tripod is mandatory and if you got it for a good price - throw it away, it is useless. It needs to be rock solid. A cable release is also needed but you can use the timer on your camera to make do in a pinch.
The next thing is to understand that there is a relationship between the F stop and the shutter speed. The longer the hole is open, the smaller it needs to be. This relationship has a bearing on how the optics work. A smaller hole has a great depth of field, i.e. more stuff will be in focus. You may not want everything in sharp focus - this applies mainly to portrait photographers.
But other photographers may also want a longer exposure - flowing water looks really cool when taken with a long exposure. But for a long exposure you may have to stop down the lense, i.e. smaller hole for the amount of light needed.
There may come a time where you are photographing a waterfall in the moonlight, you want the water to look creamy but the rocks must be razor sharp, and you can't wait all night. This is where you can play with the ISO setting. Longish exposure, small aperture, high ISO.
Don't get hung up on artifacts - there may be some but nothing that a little patience and photoshop couldn't sort out.
I'm not sure how much latitude the OP has with making the suggested adjustments with a P&S.