You can d/l the client, and if you find someone with a buddy key, you can try it out for 5 days free (my son kindly gave me his). Make sure to d/l the client first--it can take a good day or so to d/l and then patch, depending on your connection and STO's server load.
You do get bridge officers, and if you go on an away team mission, the game will give you extra security officers (in red shirts of course) to fill in the party in case you don't have enough bridge officers to fill all 4 slots. You can equip your bridge officers and set up their skills, so it's a lot more like the heroes in Guild Wars, while the security officers are like the henchmen. In space battles, you control everything.
In some missions, the game will automatically put you into an open instance and you'll be teamed up with other players who are arriving at the same time. This can be a blessing or a curse--I ended up in an instance with about 20 other players who were part of a fleet with some high-ranking players, and the instance scales with both level and number of players, apparently. When I saw we had to kill 50 Klingon ships, I about died. However, the Captains steamrolled over the enemies, and I kind of was along for the ride in that one.
It's more fun to play with Real People, but definitely doable (at least from my limited perspective) on your own.