I think we will have a lot of people chime in on this issue since we have a wide variety of posters with backgrounds in various communities. However, with that I'll attempt to start painting a picture....
Naval Aviation: For the most part as an ENS, they will be in flight school. Some of those going aviation might depart before they make the next rank (LTJG), but for the most part their time will be focused on studying and flying...and probably some sun on Pensacola's beaches!
Marine Corps: As a 2ndLT, the first assignment is The Basic School (TBS), which is approximately 6 months. They are learning how to be a platoon commanders and go through various in-depth training from spending time on live firing ranges, plenty of physical training (long marches, obstacles courses, running, etc. etc.), and learning the skills of land navigation. I'm sure someone can add much more detail to the above. However, the goal is that all officers graduating from TBS are able to lead a platoon no matter what specialty they go into after they graduate. As implied, once they leave TBS Marine officers go to specialty schools (for the most part) and those who have been selected to Marine Corps aviation commence their training in a path similar to the paragraph above; pilots will not go to their training until at least 8 months after USNA graduation.
Restricted Line & Staff Corps: Essentially is only for those medically disqualified, though not always the case. There are MANY communities under this route -- medical school to Intel.
SPECOPS: Most of the time will be spent training....SEALS, well all you need to do is look at the Discovery Channel's documentary (you can google it) and well, I think that says enough about what they do. There are other components to SPECOPS, but most of the time is spent on training and then they will eventually meet up with an operational unit and do things that...well...they normally won't talk about
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Submariners: Nuclear schooling takes up most of their time as ENS and then normally as a LTJG, they will make it out to their submarine. Once on the sub, they do some pretty cool stuff that is also not shared with the public.
Surface Warfare: Essentially, they have 3 weeks of schooling and then head directly to a ship, where, as the description you posted, they assume the role of a division officer and there are various different jobs. However, on a day to day basis, they will be learning from their Chief and Sailors about their own people, equipment, and readiness issues that he/she is responsible for. Additionally, they will be learning about various aspects of the ship to eventually be able to run the ship on behalf of the Commanding Officer (called Officer of the Deck, OOD), a very important responsibility. So basically, when ENSs show up to the ship, they know very little and over time they learn about ship operations, navigation, safety, being proactive and thinking about problems before they happen, learning how/when to make decisions on their own and when to call someone for help, so that as a "senior" ENS they earn the Captain's trust as an OOD. Surface Warfare Officers will have leadership responsibilities the minute they walk onboard; they will have leadership responsibilities as a division officer and OOD. Once they qualify OOD, it will then be their responsibility to train other officers (mostly ENS) so that they can become qualified and that is one of the awesome aspects of being a Surface Warfare Officer....you literally train those behind you....you take the knowledge and experiences of your past and pass them onto the future. The final step is to obtain the Surface Warfare Officer qualification, which is an oral board/interview/interrogation about various aspects of the entire ship (from the basic principles of how an engineering plant works to naming the current Fleet Commanders). Given that this final requirement is suppose to be completed within 2 years of arriving --- those coming from USNA will have all of this completed as an ENS. So yes, Surface Warfare Officers are busy (like the other communities) and time management/prioritization skills become a necessity! Also, given certain Combatant Command requirements for presence in their theater of responsibility, it is not uncommon for ENS to experience 1.5-2 full deployments (defined as 6 months or longer) within their first tour (27 months).
Additionally, if one chooses the Surface Warfare Officer Nuclear option, they are normally taken off the ship once they earn the Surface Warfare qualification and head to nuclear power school.
