Every state in the US except North Carolina allows a regular citizen to make an arrest if they see somebody committing a felony. In North Carolina a citizen can detain a suspect who is committing a felony, but they don't have the right to transport the person without consent. For this reason it is not technically considered a "citizen's arrest" in North Carolina.

Liability
If you are in a situation that you feel warrants a citizen's arrest you need to be careful - you don't enjoy the same legal protection that a police officer does. If you unlawfully arrest somebody, for instance, you could be legally liable.

Your liability could be both civil and criminal. This means that you could face jail time, fines, restitution and more. For this reason you should always let the police handle the situation if that is an option.

Must be a felony
The trickiest part of making a citizen's arrest is that you need to gauge the severity of the crime being committed and you should be confident that a felony is being committed. This means that you can't go arrest the neighbors for being loud (because in most areas "public nuisance" is only a misdemeanor).

Make sure you understand the situation
Sometimes what appears to be a serious crime scene actually isn't. You should only make a citizen's arrest if you feel like somebody is in immediate danger, that apprehending them is the only way to prevent the crime from taking place and if the police cannot respond in time to address the situation.

Again, because of your personal liability you should only use a citizen's arrest as a very last resort.

Procedure
Most law enforcement agencies don't publish information on how to go about performing a citizen's arrest because it often creates a dangerous situation for citizens, who are not properly trained on how to deal with situations like this.

The important elements to remember when performing a citizen's arrest is that you must tell them that you are performing the arrest and you must notify law enforcement immediately (again, you should do this before apprehending the suspect if at all possible). You can just call 911.

Also, you should never transport the suspect unless you absolutely have to. If you attempt to drive the suspect to jail, for instance, and the suspect jumps out of the car you might be liable for any injuries they sustain. It is best to just detail the suspect and wait until the police arrive.

Become law enforcement
If you are very interested in performing citizen's arrests perhaps a career in law encorcement is what you're really looking for. There are various resources online that will help you navigate the world of law enforcement careers.