It’s pretty standard MMO fare. The tutorial scenario is an alien invasion of Millenium City, where it guides you up to level 5 or 6. Most quests are “kill x” or “obtain x”, and there’s one public quest in the tutorial.
After the tutorial you can choose to go to either the US southwest desert zone or the Canadian snow forest zone for essentially tutorial part 2. This adds in crafting quests (picking a crafting discipline and focus, harvesting materials, etc.) as well as group-recommended bosses.
Basic gameplay is the same as CoX or any other MMO. Fight bad guys. Get stuff. Level up. Gain powers. Craft/obtain equipment. Repeat.
The character creator is really the best feature of CO, as it’s very detailed and very flexible, with sliders and options and sub-options and sub-sub-options for just about everything, with the inexplicable limitations on modifying non-human faces (beast, alien, insect heads, etc).
There are also no real “character classes”, as defined by most other MMOs. Instead, you either pick pre-set power sets (fire, ice, magic, martial arts, might, etc.) or build a custom set. Characters are thus defined by their stat focuses, their powers, and how they are modified. For example, two people can both have fire powers, but they can pick different types of fire powers, and they can also both modify those powers differently. One character might focus on single-target ranged attacks with their primary attack increased in level/damage; the other character might focus on close-range area attacks with damage-over-time effects added (ie clinging flames/burning).
Oh, and one aspect I think that’s handled very well is the way they give you a travel power very early (right after the first tutorial level), and that there’s no mana/endurance limit imposed by travelling. If you get flight, you can fly forever without getting tired; if you pick teleport, you’re limited to 5-second teleport bursts, but you can keep teleporting forever as long as you re-trigger the power every 5-seconds. The only penalty to travel powers is a percentage increase to the endurance costs of your other powers (typically +10% cost to other power usage).