I know what you're thinking.  Why would we not know our class?  Well, young grasshopper, take a trip through the Random Dungeon Finder at any level, run a couple dungeons of any type and I can assure you that you will find at least 1-2 people in your endeavor who have no idea how to play their class.  To be honest, mages kind of have it easy.  We don't have to figure out how to keep other people alive; we're DPS all the way.  Classes like Paladins and Druids have to figure out how to do 3 different roles and classes like Shaman and DKs have to figure out how to do 2.  Hybrids do have it harder in some cases, so we'll break this down into a question:

Are you a tank, healer, physical DPS or caster DPS?  Physical DPS could further be broken down into hunters and melee if you like.  For each role, there are ground rules.  Caster DPS, hunters, and healers stand at range in most cases.  The rocket science behind this is that there's a magical range at which aggro is drastically decreased, so standing at range = less threat = happy healer = less death.  Melee DPS and Tanks obviously have to stand close to the target cause they can't swing their weapons that far.  Yes, this also exposes them to higher threat levels, but that's probably why most of them wear plate or have some pretty big threat reduction.

Besides range, there's the obvious point of each role.  Tanks take damage and keep the bad guys from pwning the rest of the group.  Healers keep everyone alive.  DPS kills stuff.  Sometimes these roles aren't as concrete, like when a healer is struggling a DPS who has the ability to heal can toss out a heal to help or when a healer gets bored, maybe they'll put some DPS on something, or sometimes DPS end up tanking like on Prince Keleseth in ICC for a shadow priest or warlock.  Beyond that, everyone pretty much stays in an assigned role and doesn't deviate.

An important part of knowing your class is knowing your buttons.  And by buttons I mean your cooldowns, escape tricks, and fun little abilities that benefit your role or the group/raid as a whole.  Some of these are essential to staying out of fire.  Others are important to prevent a wipe.  Others just make you do your job a little faster or harder, essentially better.  Figure out what those are and the ideal time to use them.  

To be honest the best way to learn a class is to play it from 1 to 80 (or 85 come cataclysm) but there's some things you won't learn just questing or just doing dungeons or just PVPing.  It's really a mixture of these that makes you aware of all the skills you have available to you and where you belong in the scheme of things.

We'll use mages as an example here because that's what I blog the most about.  Every class has 3 available specs.  Each one has a specific role assigned to it, sometimes two in the case of feral druids.  For mages, all 3 are DPS, so you get a choice of DPS or DPS... or DPS.  And we're always caster DPS, despite how much fun it may be to stab someone with your Quel'Delar or crack them over the head with your Abracadaver.   Anywho, Mages get a choice of Fire, Frost, and Arcane.  If I were to research the aspects of each spec, here's what I'd look for:

When I say test it, I don't mean in one single medium or situation.  When I get a new spec, I first like to try it on a training dummy so I can get a hang of the rotation without any distractions like fire to stand in or things to dodge or threat that gets pulled.  The problem with training dummies is that they don't always give you an accurate read of your DPS.  When you're playing with a dummy, you're standing still, DPSing with no downtime.  There's no raid mechanics to make your DPS higher or lower.  There are also things about the dummy that are going to throw off about your DPS.  For example, frost mage DPS is actually slightly lower than it should be on a dummy because they are susceptible to stuns, so the big hit of Deep Freeze isn't a bit hit.  It's a stun with no damage.  Because of this, if you have the Deep Freeze glyph, your frostbolt is also going to hit harder than it actually would on a boss, since bosses don't retain the Deep Freeze debuff. (This glyph is changing to be more useful and more appropriate to a prime glyph in the Cataclysm Beta.)

After you've fiddled around with the dummies for a little bit, go out and solo.  Play with a few mobs you know you can kill and compare the timeframe it took you before and after.  Try some that were more difficult for you before.  Put yourself in some situations where you have to move and fight and maybe use some of those special buttons.  

After you've done all this without endangering the life bars of your fellow players, take it into a heroic, either with friends or a PUG.  Don't just run one, run several.  The nice thing about the variety of heroics we have at 80 is that it's never the same instance twice: the pacing is different, the boss gimicks are different, and the levels of difficulty are different.  Once you've messed around enough in an instance, you can try a raid, but if I were you I'd make it a raid with friends or a raid like VOA that's short and sweet.  Never ever ever take a new spec you're not completely comfortable with into a progression raid where you're expected to perform your best.

You're basically going to do all the stuff you did in step 3, but in a different spec.  For some classes, this may require a whole different set of gear, but if it's generally the same thing, you can share it.  Keep in mind that testing healing and tanking is very different from testing DPS.  You can't use a dummy to check healing where rotations are completely useless.  And dummies don't have threat, so while you can check your tanking rotation, it won't be as accurate as doing it on something that actually does damage back to you.  But even with tanks and healers, the don't raid till your comfortable with your spec rule stands.

I can almost guarantee you that playing a spec you enjoy is going to give you better results than playing something you don't like at all.  In some cases this may change (ie Old Frost Mages) and you may have to pick your second favorite thing to do.  In the cases of raiding guilds, you may not have a choice because in those kinds of guilds they're allowed to tell you what to play.  But if you don't like it, then don't be in that guild or try a different class that can fill the role that they need.  A good guild will be patient with a player who hasn't found their niche yet and will understand that in the end they'll get better performance out of a happy player than someone who's miserable.

The tweaking part of this step is not always easy, but no two players play alike, so following a guide to the letter is not always your best bet for maximum performance.  Beyond that, we all play on different machines with different connections in a variety of different real life situations, so that's going to affect your performance too.  You really do have to pick what works for you.  Do you have any motivation to play something that you hate?

My best advice for someone who is being pressured into something different is to try it first, especially if changes have been made or you're character has changed.  I used to hate fire with a passion and had no desire to do anything with it.  Now that the specs have changed so much since pre 4.0.1, I actually enjoy Fire again and have put Arcane on the back burner so that I can play with it or Frost as my heart so desires.  Because I made that decision for myself, I'm a happier player and it's important to remember that WoW is a game, so all other things aside, it should be fun.