My aim is to give a high-level overview of the Duty Officer system to start with and use any questions/comments to guide further delving.
What is the Duty Officer (DOFF) system?
Well, at its core, it is an entirely optional minigame. But it does tie into the newly revamped R&D system (Crafting) and the Fleet Starbase and the assorted holdings.
Why should I care?
As mentioned above, at the very least it is tied into the Fleet Starbase system and the R&D system. Pulling back a little bit, it can be an alternate/supplemental source of: Dilithium, XP, Fleet Marks, commodities, raw materials, and gear*.
*due to the rng nature of the rewards from DOFF crafting missions, the proliferation of fleet gear/rep gear, and the new R&D system, your mileage may vary on your rewards.
Ok, so how does this all work?
Depending on where you are in the galaxy and what time it is, a random assortment of DOFF missions will be available for you to choose from. As you find missions you'd like to run, you assign DOFFs from your crew, then sit back and wait for the mission timer to finish (just like rep and starbase projects).
Wait...where I am in the galaxy? And what time of day it is?
Yes, every 4 hours the list of available DOFF missions in each Sector Block and most social maps updates. So the list of missions available on Earth Spacedock from 12PM - 4PM will differ from the list from 4PM - 8PM, and so on. The Personal mission list updates every hour. And the missions available from your Department Heads updates on a 20 hour rotation and is affected by where in the galaxy your are.
You expect me to tour the galaxy every 4 hours?
In reality: no. Here is where we can leverage the power of the community. With the help of Captains like you, a Google Spreadsheet (http://bit.ly/DOFFS) has been created to easily show which missions are currently available and where. While not mandatory to use in conjunction with the DOFF system, it can help streamline your efforts.
Whoa...spreadsheets, timers, this is starting to sound a bit too complicated...
On the surface and taken as a whole, yes, it can seem complicated and overwhelming. But it needn't be. It can be as simple or as complicated as you want it to be. If you just want to use the default DOFFs and worry about missions once a week, you can. Do you want to micromanage every minute of each of your DOFF's lives every time you log in? Or any other variation? You can. Lots of room out there in the black for everyone.
Alrighty, hopefully I haven't turned anyone off of the DOFF system forever. I promised I wouldn't muddy the waters by going too in-depth to start, so feel free to respond with questions/comments and we'll see where we end up.