Like this, only... well... Okay, exactly like this. Exactly.
It's important to choose a power that conforms to your style of play. There are six different power sets available in DCUO; Fire, Ice, Nature, Sorcery, Mental, and Gadgets. These powers dictate your role, which is either defender, healer, or controller, respectively. Each role can switch to a DPS stance between battles, but that's really only good for solo play. You can roll DPS in a group, but it's sort of frowned upon.
Joey and I both said "eff it" and rolled DPS almost exclusively all the way to the level cap. You can hit level 30 pretty easily in DCUO, even if you're flying solo. Since we both had the same mentor, we both followed the same story arc. So we were able to co-op the entire campaign. You can participate in other players' story arcs, but it won't advance your own story unless you have the same mentor.
We would play our defensive and healer roles whenever we grouped with other people, because we are team players when we need to be. Especially when we required more than two people to complete a mission, or when other players screamed at us to play our roles. After the early hiccups we became quite skilled at either drawing aggro, healing, or simply muting other players.
The need for teamwork became apparent as soon as we hit the level cap. Roughly half the missions in DCUO aren't accessible until you reach level 30. As soon as these bad boys open up, you better have some friends to raid with. High level instances, called 'Alerts' and 'Duos', are perfect for co-op play. Alerts are for four players, and it's essential that everyone plays their role, or you'll be respawning constantly. Thankfully, there's no penalty for getting K.O.'ed, unless you count the crushing feeling of absolute failure.
The meta power Iconic Armor sets look like this. You have to have them
Duos are the meat of two player co-op play. These are high level missions built for two (and only two) players. Joey and I formed our own dynamic duo. We'll just say that he was my side kick, because he's not here to defend himself. Completing these Duos reward players with Marks of Triumph, which can then be used to purchase pieces of the Iconic Armor Tier 1 set. These iconic armor sets are the most powerful in the game, and they come in three flavors. Awesome PvE (player versus environment, if you're greener than Alan Scott), Awesome PvP (player versus player) or Even Awesomer PVE. They are styled after whichever major DC hero of villain you chose as a mentor.
Once you get all the Tier 1 PvE armor you're tough enough to go on high level Raids, which is where you get Marks of Distinction, which will allow you to purchase pieces of the Tier 2 PvE armor. You need eight players working together to complete these. By the time you're at this level you should have received a handful of invites to a league (dozens, if you're character is female) where you should be able to find plenty of willing raiders. DCUO is full of end game content, and you have to co-operate to complete it. You can only do one raid a week, and five Duos a day. If you do the math this equals beau coup bucks in subscription fees, months of time, and incalculable loss of love life.
I myself collected a few pieces of Tier 1 armor, then had to move on to other games due to my awesome obligations at Co-Optimus. I planned to get back to the game, then the PSN got hacked, so I haven't been on DCUO for a while now. I didn't realize how much I missed it until I couldn't have it. I know I have a free month coming once the PSN is back up and running. I've heard they've increased the amount of Duos...