This area of law is very complex and the following is only basic guidance. The law states that,

Any person can arrest a person who is in the act of committing an indictable offence or
Anyone whom he reasonably suspects to be committing such an offence, if
it is not reasonably practicable for a constable to make the arrest instead and
it is necessary to arrest the person for one of the below reasons,

To prevent the person in question,
causing physical injury to himself or any other person;
suffering physical injury;
causing loss of or damage to property; or
making off before a constable can assume responsibility for him.

There a few points to raise about the above paragraph.
1. What is an indictable offence?
An indictable offence is an offence that can be tried at Crown Court. Below are examples of indictable offences which are the most likely to be encountered by members of the public,
-criminal damage.

2. How do I know if I can make a citizens arrest?
You can make an arrest if the suspect is actually committing the offence or if you reasonably suspect them of committing it, or when the offence has been committed and you reasonably suspect them of having committed it. There is no specific wording to use when making a citizens arrest. However you must inform the person you are arresting as soon as possible what you are doing, why you are doing it and what offence you believe the person has committed. There are other considerations to make when making an arrest,
reasonable force – see question in related information for details on reasonable force.
potential for civil litigation – the courts are sympathetic to public spirited citizens and the exercise of their powers and rights, however, if you get it wrong you could be sued for unlawful arrest and/or false imprisonment.
do not make a citizens arrest if you feel that you would be putting yourself or any other person in danger, ring 999.