So, does the assassination kill always work or do you need to be able to deal enough damage to kill the person?
You have to deal enough damage to kill the target. Please note that you CAN use power attacks. Also, you won't ALWAYS get the animation, I think it's a bit random whether you do.
Could you kill a hard boss with a weak iron dagger, or do you need the best?
It depends on a lot of other factors, such as your level (and therefore the boss's level), your skill with daggers and sneak (multiplier on daggers), perks you picked, poisons/enchantments used, etc. in theory, it is possible, but the better your weapon (and all other aforementioned things), the better your chances are.
Also, I couldn't get it to work when wielding the dagger in my left hand. Does it have to be right?
Yes, it has to be right
I love doing assassination kills too. I once killed a dragon priest that way, and the final spirit enemy in... volunruud I think it was. : )
Edit: One great tactic I love to use is to sneak, shoot someone with an arrow, hide as they try to find you, and as they start to walk away I sneak up behind them and slit their throat. Very effective, and fun!
Sounds cool