[Intel Source: The Sub Report] Check out this fairly lengthy (5+ minute) video of USS Wyoming (SSBN 742) submerging, as seen from the periscope:
While it's clear that Ohio-class boats aren't the quickest-diving boats in the world, it always seemed to me like it took my attack boats a long time to dive -- maybe it's just because you're so focused on listening to everything that's going on around you while you're looking through the 'scope that it just seemed like it took forever. Non-submariners will be interested in the water shooting up from either end of the boat -- that's the air being expelled from the ballast tanks as the water pushes in from the bottom.
The OOD's main responsibility after he gives the order to the DOOW to "Submerge the ship" is to call "Decks awash". I always thought that this was more of an art than a science; you can't do it when the water is first washing across the deck, but if you wait too long it ends up taking forever to get down. I never had the CO yell at me for doing it wrong, though, so I guess I had a good feel for it (either that, or it doesn't matter as much with the boats being so big nowadays). I somehow ended up with more than my share of diving (and surfacing) evolutions as a JO; I probably did about 15 or 20 of each as OOD -- plus over 100 trips to PD. I kept trying to tell the pilots I worked with on the carrier that I should get as much respect for that as the guys who celebrated their 100th carrier trap, but none of them ever believed me.