how do octopuses move through the water?

They use their arms to pull themselves around the bottom or they can use their 'umbrella' to propel themselves like swimming.
If threatened, they can use a jet of water and ink to rocket away from danger and hide:
https://www.youtube.com/watch?v=3Sn_RruRKts
They are not only smart, they are masters of camouflage. Changing colors and patterns before your eyes to blend in with their background. Certainly one of my favorite marine animals.

They may crawl on the bottom or they may use jet propulsion by expelling water from their siphon. Some, like the dumbo octopus, also have fins, that they can use to swim.