For any player new to raiding, the biggest hurdle they will initially face is the fact that their skills might not be enough for a demanding raid leader. This is especially true in the case of hybrid classes like the Paladin, Druid, and Shaman who may be asked to shift specs and totally alter their playing style for the greater good of the raid. If you are new to the raid and want to prove yourself worthy and deserving of a permanent spot in the raid, you will need to be flexible and willing to learn.
However, in some cases, you will not be expected to change your playstyle too drastically. For instance, pure damage dealers like the Rogue, Hunter, Warlock and Mage have roles in a raid that do not change too much, besides the odd request to change specs to unlock certain abilities for specific situations. In this case, they will need to concentrate on improving their DPS. This usually involves using more effective spell rotations and learning their class inside out.
However, those of you out there with hybrid classes such as the Paladin, Druid, Shaman, or Death Knight (and sometimes Priest), will find that your role in the fight becomes much more fluid. In some fights, a DK or Druid might prove to be a more effective tank for resistance reasons while Shamans might be great at support in one fight and work as off healers in another fight.
The long and short of it is that if you have abilities that work for tanking, dps and healing together on your character, you should be ready to use any of them at any time.
In a raid, once the fight is started, you'll almost always have a set position to work on. You're not going to be tanking for one trash mob, then DPS for the next and then Healing on a boss. But, between bosses or instances as a whole, you might find that the needs of your raid party change and that is when you should be willing to switch.
Another thing to remember is the need to be honest at all times. For instance, if you are a Holy Paladin who is clueless about tanking, you will need to come clean immediately. This will help you avoid embarrassing situations especially if you fail at the task repeatedly, thereby earning the wrath of your teammates and more importantly, the raid leader.