There's a demo that showcases a couple of the platforms if you have broadband and can download it.
http://www.scs-dangerouswaters.com/demo.html
A typical games starts with you picking a platform (air, surface, or sub), reading a quick mission brief and mission objectives, and starting the mission. At the start of the mission I typically zoom around the stations abit looking at all the sensors see what and who is already in sensor range, as well as a feel of the overal situation, using the sonar, ESM, periscope, etc to get a feel of the environment at missiostart.
After that you go from there, with whatever strategy you need to complete the mission objective.
In every mission your the captain. You can play at various levels of automation, with your crew AI detecting the sonar contacts, determinating their ranges and courses, and plotting weapon trajectories, with you only giving the orders. Or you can play with more microcontrol doing some of the stations yourself if you feel like it (or feel you can do a better job.)
If you feel like cheating you can "show truth" and get the skimmy on all the contacts in the area as well as the enemy location. Or you can do it the hard way and find it all out yourself, and check how accurate you were later with the mission replay showing the real deal.
Hope that helps.
lb
ps) the campaign is a linear series of missions based on a storyline, with objectives you must complete with each mission.