| It is probably easiest to define a card counter as a person who uses a method of counting the cards in their mind (described fairly well in counting cards) to give themselves an advantage at blackjack. They can be anyone, and chances are you wouldn't know one if you were sitting next to them. Watch the eyes, at a full blackjack table. The counter's eyes will always follow all the cards being dealt.
This is the procedure at the Casino in which I worked security, which can't be named, of course. Procedure will differ from casino to casino, and from country to country, as best befits the gaming laws of the area.
Card counters are cheaters. As such, they're treated much like any other cheater is treated, with special considerations. Because card counting is not very visible, most of the procedure involving a card counter is silent. That is to say, nothing happens unless he's being blatantly, horrifically obvious, counting numbers aloud.
First, surveillance will take a snapshot of the counter. They get his face, along with any other pertinent information. For example, if he has a preference towards a particular table, pit boss (or supervisor, if the name has been retired), dealer or pit. Various information is kept on hand, as well. For example, if the counter is a drunk, under the influence in any way.
If he's a very obvious cheater, his picture may be sent to other casinos in the area. At this point, it may become necessary to check other casinos to see if he's been caught for any offences, like being disorderly, or cheating. If the counter is well-known, he won't be barred from the casino, but surveillance will be told (by whoever is having the problem with the counter) to notify security, and security will keep an eye on him.
No temporary bans are placed on card counters, if they are ejected from the casino. Bans are permanent.
I apologize for using the masculine, but I don't like using he/she, or s/he, and it's usually men who count cards.
Disclaimer: I wouldn't suggest using this information to your advantage, either. I'm going to assume that getting thrown out of a casino on your head is rather embarassing.
Further disclaimer: This information is factual according to the House's rules, at the casino where I was once an employee. Again, I say: The House's decisions are final. | 
