1. One stat can have a total of 255 EVs. But since roughly four EVs equals one stat increase (thanks TwilightBlade for that bit of info), most just train to 252 and use the remaining EV's in another stat. Once all 510 EVs are filled up, you are done EV training.
2. EV trained Pokemon are much better in competitive battling compared to non-EV trained Pokemon because EV trained Pokemon have been trained to excel more in a specific stat, as opposed to non-EV'd Pokemon where their EV's are spread out or have none at all. Also, if you didn't keep track of your EV's for a non-EV trained Pokemon, a physical sweeping Pokemon could have EV's in special attack, which is incredibly pointless.
3. Once you've filled up all 510 EVs, you can just focus on leveling up your Pokemon for attacks that it may need. It won't lose or gain any EVs.